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ISOMETRIC  DRAWING 


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\rttttttiitttto*ttittttf\t)t*ttttt*tttttt*t*ftttt 


ISOMETRIC  DRAWING 

A  TREATISE  ON   MECHANICAL  ILLUSTRATING 
DEALING  WITH  TYPICAL  CONSTRUC- 
TIONS   AND    OUTLINING 


A  COURSE  IN  THE  ART 


BY 


ALPHA  PIERCE  JAMISON,  M.E. 

Professor   of  Mechanical   Drawing,    Purdue    University ;     Junior  Member   of  the 

American   Society   of  Mechanical   Engineers;     Author  of    "Elements   of 

Mechanical  Drawing"   "  Advanced  Mechanical  Drawing,"  etc. 


MCGRAW-HILL  BOOK  COMPANY 

239  WEST  39TH  STREET,  XEW  YORK 

6  BOUVERIE  STREET,  LONDON,  E.C. 

1911 


Copyright,  1911 

BY 

McGRAW-HILL    BOOK    COMPANY 


PREFACE 

THE  writer  has  been  a  teacher  of  mechanical  drawing  since 
the  year  1895;  during  this  time  it  has  been  his  privilege  and 
pleasure  to  instruct  many  students. 

As  a  part  of  the  course  administered,  each  student  has  been 
given  some  instruction  and  practice  in  Isometric  Drawing;  this 
practice  has  been  limited,  because  of  lack  of  time  to  devote  to 
it  (most  of  the  time  assigned  being  given  to  straight  mechanical 
drawing),  but  has  always  been  of  interest  to,  and  appreciated 
by,  the  student. 

Isometric  Drawing  is  growing  in  popular  usefulness,  and  one 
can  hardly  pick  up  a  technical  paper  or  magazine  without 
finding  one  or  more  examples;  its  convenience  and  its  adaptabil- 
ity are  being  recognized,  and  a  knowledge  of  its  execution  is 
desirable  and  necessary  for  all  draughtsmen. 

All  treatments  of  the  subject  known  to  the  writer  accompany 
a  treatise  on  Descriptive  Geometry,  or  are  too  short;  in  every 
case  the  subject  is  treated  with  more  attention  to  theory  than 
to  its  practicability. 

The  broad  field  for  its  use,  its  growing  popularity,  the  enthu- 
siasm with  which  a  student  "  takes  hold,"  and  the  nature  of  the 
present  (known  to  the  writer)  texts  on  the  subject  have  led  the 
writer  to  believe  that  a  plain  exposition  of  the  "  How  "  of  the 
art,  with  no  reference  to  the  "  Why,"  may  be  of  some  service 
to  teachers,  students,  and  draughtsmen. 

It  is,  therefore,  with  the  object  of  presenting  the  subject 
in  a  new  light  or  way,  in  the  hope  that  others  may  find  the  art 
as  useful  as  the  writer  has  found  it,  in  the  hope  of  service,  and 
not  in  the  nature  of  a  "  This  is  better  than  thine  "  spirit,  or  in 
criticism  of  what  has  been  written,  that  this  work  is  offered. 

A.  P.  JAMISON. 

PUHDUE  UNIVERSITY,  WEST  LAFAYETTE,  IND., 
June  13,  1911. 

v 


227947 


CONTENTS 


CHAPTER   I 

PRELIMINARY  DISCUSSION  AND  EXPLANATIONS 

SECTION  PAGE 

1.  Introductory 1 

2.  Definitions 1 

3.  Uses  of  the  Art 3 

4.  Time  element 8 

5.  Characteristics 9 

6.  Tools  used 10 

7.  Center  lines  and  axes 11 

8.  Flexibility 12 


CHAPTER   II 
THE  DRAWING  OF  PLANE  FIGURES 

9.  To  draw  a  square 16 

10.  To  draw  a  hexagon 16 

11.  To  draw  an  octagon t  18 

12.  To  draw  any  polygon 19 

13.  To  draw  a  circle 20 

(a)  First  method 20 

(6)  Second  method 22 

(c)  Error  of  the  first  method 22 

(d)  To  draw  an  inscribed  hexagon 24 

(e)  To  draw  a  circumscribed  hexagon 24 

(/)   To  draw  a  series  of  circles 25 

14.  To  draw  an  ellipse 26 

15.  To  draw  an  hyperbola 27 

16.  To  draw  a  parabola 27 

17.  To  draw  an  undulating  figure 28 

1 8.  To  draw  any  figure  composed  of  straight  lines  and  circular  arcs 28 

19.  The  proper  arrangement  of  all  drawings  with  reference  to  the  center 

lines,  and  the  manner  of  laying  off  dimensions 30 


viii  CONTENTS 

CHAPTER   III 

THE  DRAWING  OF  SOLIDS 
SECTION  PAGE 

20.  Preparatory 32 

21.  To  draw  a  rectangular  block 33 

22.  To  draw  a  pyramid  of  blocks 34 

23.  To  draw  an  hexagonal  prism 35 

24.  To  draw  an  hexagonal  pyramid 35 

25.  To  draw  any  rectangular  solid  which  is  of  uniform  or  similar  section .  36 

26.  To  draw  any  rectangular  solid  of  variable  section 38 

27.  To  draw  a  cylinder 39 

28.  To  draw  a  cone 40 

29.  To  draw  a  solid  made  up  of  circular  arcs  and  straight  lines 40 

30.  To  draw  a  ring,  rectangular  in  section 41 

31.  To  draw  a  circular  disc  with  holes  in  it 43 

32.  To  draw  a  stepped  pulley 44 

33.  To  take  out  a  section 45 

34.  To  draw  an  eccentric 46 

35.  To  draw  an  hexagonal  nut 47 

36.  To  draw  a  hollow  cylinder  with  a  section  removed 48 

37.  To  draw  any  solid  of  revolution 49 

38.  To  draw  a  ring,  circular  in  section 51 

39.  To  draw  screw  threads 51 

40.  To  draw  a  sphere 54 


CHAPTER   IV 
A  COURSE  IN  ISOMETRIC  DRAWING 

41.  Explanatory 57 

42.  Sheet  No.  1, 

Isometric  drawings  of  some  plane  figures 58 

43.  Sheet  No.  2, 

Isometric  drawings  of  some  straight-line  objects 60 

44.  Sheet  No.  3, 

Isometric  drawings  of  some  bench  exercises 62 

45.  Sheet  No.  4, 

Isometric  drawings  of  some  cylindrical  objects 64 

46.  Sheet  No.  5, 

Isometric  drawings  of  some  shop  tools 66 

47.  Suggested  sheets 68 

48.  Remarks, 

Dimensioning 68 

Enlargement 68 

Distortion 68 

Shading 69 


ISOMETRIC  DRAWING 


CHAPTER  I 
PRELIMINARY   DISCUSSION   AND   EXPLANATIONS 

1.  Introductory. 

To  understand  what  is  to  follow,  the  reader  must  possess  a 
working  knowledge  of  mechanical  drawing;  assuming  this  much, 
then,  it  is  proposed  to  present  the  Art  of  Isometric  Drawing 
with  but  very  little  preliminary  or  preparatory  explanation. 
Attention  is  to  be  given  to  the  way  in  which  a  drawing  can  be 
made,  rather  than  to  the  reasons  for  doing  "  thus  and  so." 

Plain  and  common  terms  will  be  used  in  so  far  as  they  can  be 
found  to  fit,  and  in  the  event  a  few  unfamiliar  words  are  used 
they  must  not  be  allowed  to  affect  the  reader's  interest;  as  a 
matter  of  fact,  the  art  is  so  simple,  having  but  two  principles 
or  characteristics,  that  any  draughtsman  should  have  little, 
if  any,  difficulty  in  acquiring  it. 

Students  are  urged,  therefore,  to  read  this  work  through 
carefully,  to  study;each  successive  step,  as  the  subject  is  developed, 
to  draw  for  themselves  the  several  explanatory  figures  given 
in  the  text,  and  to  further  their  working  knowledge  by  the 
execution  of  the  few  plates  given  for  this  purpose  in  Chapter 
IV.  Such  attention  will  cover  all  of  the  essentials,  and  should 
furnish  a  knowledge  of  the  art  sufficient  for  practical  use. 

2.  Definitions. 

From  an  engineer's  standpoint  (so  designated  to  distinguish 
it  from  the  artist's  standpoint),  Drawing  is  divided  into  four 
main  divisions,  namely:  Mechanical  Drawing,  Perspective  Draw- 


2    "    " 


DRAWING 


2 


\ 


PLATE  No.  1. 


PRELIMINARY  DISCUSSION   AND    EXPLANATIONS  3 

ing,  Isometric  Drawing,  and  Cavalier  or  Cabinet  Projection 
or  Drawing. 

Mechanical  Drawing  is  the  art  of  drawing  each  separate 
face  of  an  object  just  as  it  is  and  not  as  it  appears,  and  arrang- 
ing the  several  drawings  so  as  to  show  the  relation  of  the  faces 
one  to  the  other;  Perspective  Drawings  are  the  same  as  pictures, 
and  show  the  object  as  it  appears  from  a  definite  viewpoint; 
Isometric  Drawing  is  a  kind  of  mechanical-perspective,  or 
picture;  and  Cavalier  Projection,  a  kind  of  mechanic al-isome trie- 
perspective  drawing. 

Plate  No.  1  illustrates  the  four  kinds  of  drawings,  Fig.  1 
being  a  two-view  mechanical  drawing,  Fig.  2  (A  and  B)  a 
perspective  drawing,  Fig.  3  an  isometric  drawing,  and  Fig.  4 
a  cabinet  drawing.  The  mechanical  drawing  requires  two 
views  to  show  the  object  (a  part  of  a  core  box),  while  the  per- 
spective drawing  (Fig.  2  A),  shows  it  in  one  view. 

In  the  mechanical  drawing  all  parallel  lines  of  the  object 
are  drawn  parallel;  in  the  perspective  drawing  three  faces  of 
the  object  are  shown  in  one  view;  in  the  isometric  drawing 
three  faces  of  the  object  are  shown  in  the  one  view,  and  all 
parallel  lines  of  the  object  are  shown  parallel  in  the  drawing; 
in  the  cabinet  drawing  one  face  of  the  figure  is  drawn  as  in  the 
mechanical  drawing,  all  parallel  lines  of  the  object  are  parallel 
in  the  drawing,  as  in  isometric  drawing,  and  the  figure  shows 
three  faces  in  one  view,  the  same  as  the  perspective  drawing. 

While  it  is  true  that  one  must  have  a  knowledge  of  mechan- 
ical drawing  in  order  to  make  an  isometric  drawing,  the  very 
opposite  is  true  as  to  the  reading  of  the  two  drawings,  as  one 
with  no  knowledge  whatsoever  of  the  principles  of  mechanical 
drawing  is  able  to  readily  read  an  isometric  drawing.  A  per- 
spective drawing  is  easily  read  by  all,  but  it  is  hard  to  make 
unless  one  is  more  or  less  of  an  artist  at  free-hand  work;  an 
isometric  drawing  is  easily  made  and  readily  read  by  all. 

3.  Uses  of  the  Art. 

Being  familiar  with  the  principles  of  mechanical  drawing, 
the  reader  is  also  acquainted  with  the  wide  field  for  the  use  of 


ISOMETRIC  DRAWING 


fe       a 

o    y 

o 


I     f 

g      3 


PLATE  No.  2. 


PRELIMINARY  DISCUSSION  AND  EXPLANATIONS  5 

such  drawings,  for  manufacturing  and  erecting  purposes,  in 
the  shop  and  in  the  field,  in  books  and  catalogues,  etc.  Per- 
spective drawing  is  not  much  used  in  engineering  drawing,  its 
field  being  practically  limited  to  architectural  work.  It  is 
often  desk-able  to  "  picture  "  a  machine  or  machine  part  or 
other  object,  and  because  of  its  adaptability  it  is  here  that 
isometric  drawing  finds  its  use. 

Plate  No.  2  illustrates  a  three-view  mechanical  drawing  of 
a  bench-lathe  leg,  a  perspective  drawing  of  the  leg,  and  an 
isometric  drawing  of  the  leg.  A  mechanical  drawing  is  pri- 
marily a  working  drawing  and  lends  itself  to  dimensioning; 
a  perspective  or  isometric  drawing  is  primarily  an  illustration 
or  picture  and  is,  in  most  cases,  difficult  to  dimension.  In  fact, 
a  perspective  drawing  can  hardly  be  said  to  lend  itself  to  dimen- 
sioning at  all;  an  isometric  drawing  will  permit  dimensioning, 
though  it  is  seldom  done. 

Because  of  its  similarity  to  perspective  drawing  and  of  the 
manner  of  execution,  isometric  drawing  is  sometimes  called 
"  Mechanical  Perspective."  Examples  of  its  use  are  shown  as 
follows: 

Fig.  1 1  is  a  copy  of  an  illustration  appearing  in  the  Proceed- 
ings of  the  American  Society  of  Mechanical  Engineers  (Vol.  29, 
page  172),  and  is  one  of  four  similar  cuts  illustrating  a  paper 
on  the  "  Cost  of  Heating  Store-houses." 

Fig.  2  2  is  a  copy  of  an  illustration  appearing  hi  a  catalogue 
issued  by  a  manufacturing  company  of  their  metal  lumber, 
showing  the  framing  of  a  house  with  then*  product. 

Fig.  3  is  an  isometric  drawing  detailing  the  entrance  to  a 
building. 

Fig.  4  is  a  "  bird's  eye  "  view  of  an  athletic  field  showing 
the  enclosing  wire  fence,  the  bleachers  and  grandstand,  the 
foot-ball  and  base-ball  fields,  and  the  running  track. 

It  is  for  such  work  as  is  illustrated  by  the  just  mentioned 

1  Reproduced  by  permission  of  the  American  Society  of  Mechanical  Engi- 
neers and  of  Mr.  H.  O.  Lacount,  Boston,  Mass.,  author  of  the  paper  mentioned. 

2  Reproduced  by  permission  of  the  Berger    Manufacturing    Company, 
Canton,  Ohio. 


ISOMETRIC    DRAWING 


FIG.  1. 


FIG.  2. 


PRELIMINARY  DISCUSSION   AND   EXPLANATIONS  7 

figures  that  isometric  drawing  finds  its  ready  and  best  use, 
that  is,  in  drawings  where  most  of  the  lines  are  straight  lines 


FIG.  3. 


and  the  objects  drawn  are  of  a  rectangular  character.  It  is 
possible,  however,  to  draw  many  kinds  of  irregular  objects, 
as  is  evidenced  by  the  illustrations  of  the  text. 


8 


ISOMETRIC  DRAWING 


4.  Time  Element. 

While  isometric  drawing  is  limited  to  certain  uses  because 
of  the  nature  of  the  object  and  the  purpose  of  the  drawing, 
the  real,  practical  limitation  to  the  art  is  the  time  required  to 
execute  the  drawings. 

The  author  has  on  several  occasions  made  comparison  of 
the  time  required  in  which  to  draw  a  mechanical  drawing  and 
the  time  consumed  in  making  an  isometric  drawing;  he  has 
timed  himself,  and  has  taken  the  time  of  a  number  of  students, 
and  finds  that,  with  the  exception  of  very  simple  rectangular 
objects,  it  requires  more  time  to  make  an  isometric  drawing 


FIG.  4. 

than  it  does  to  execute  a  mechanical  drawing — the  increase  in 
time  required  depending  entirely  upon  the  nature  of  the  object. 
For  some  very  simple  objects  it  was  found  that  an  isometric 
drawing  could  be  made  in  a  little  less  time  than  that  required 
for  making  a  mechanical  drawing;  for  a  large  number  of  simple 
rectangular  objects,  with  few  curves  and  circular  holes  or 
cylindrical  parts,  it  was  found  that  the  time  required  for  the 
two  kinds  of  drawings  about  balanced;  as  the  object  drawn 
became  more  complex,  having  cylindrical  and  curved  members, 
nuts,  threads,  etc.,  to  draw,  the  time  required  varied  from 
30  to  200  per  cent  more  time  for  isometric  drawings  than  for 
straight  mechanical  drawings,  the  average  being  about  80  per 
cent. 


PRELIMINARY  DISCUSSION*   AND    EXPLANATIONS 


9 


In  general,  therefore,  it  may  be  said  that  isometric  drawing 
requires  from  50  to  100  per  cent  more  time  for  its  execution 
than  mechanical  drawing.  Of  course,  some  objects  will  require 
several  hundred  per  cent  more  time;  but  it  is  surprising,  in 
the  field  for  which  it  is  best  adapted  and  for  the  purpose  for 
which  the  drawing  is  most  used,  how  many  illustrations  may  be 
made  with  isometric  drawings  with  but  very  little  increase  in 
time  taken  over  that  required  for  making  a  mechanical  drawing. 

5.  Characteristics. 

It  has  been  stated  (Article  1)  that  isometric  drawing  has 
but  two  principles.  Such  a  statement  is  speaking  broadly,  and 


FIG.  5. 


should  be  further  qualified  by  adding,  "  which  are  new  to  one 
already  familiar  with  the  principles  of  mechanical  drawing." 

Isometric  drawing  is  based  on  isometric  projection,  and 
isometric  projection  is  the  result  of  a  particular  kind  of  pro- 
jection and  has  a  certain  definite  underlying  principle.  This 
work  being  an  exposition  of  the  "  How  "  of  the  art,  the  develop- 
ment and  the  further  explanation  of  the  theory  are  purposely 
omitted. 

In  mechanical  drawing  the  center  lines,  dimensions,  and 
reference  lines  are  drawn  horizontally  and  vertically,  and  a 
view  is  given  for  illustrating  each  face  of  the  object  drawn; 
in  isometric  drawing  the  center  lines,  tlimensio.ns-aftd-retefence 
lines  are  drawn  at  an  angle  with  the  horizontal  and  vertical, 


10 


ISOMETRIC  DRAWING 


and  three  faces  are  shown  in  one  view  or  drawing.  The  two 
characteristics  of  isometric  drawing,  as  compared  with  ordinary 
mechanical  drawing,  are,  therefore,  the  direction  of  the  principal 
lines  and  the  showing  of  the  three  dimensions  of  an  object  in 
one  view.  (See  Fig.  5.) 

6.  Tools  Used. 

The  tools  required  for  making  isometric  drawings  are  prac- 
tically  the   same    as   those   needed    for    ordinary    mechanical 


FIG.  6. 


FIG. 


drawing  (Fig.  6),  the  only  difference  being  in  the  triangles. 
The  principal  lines  in  isometric  drawing  are  either  horizontal, 
vertical,  or  30°  or  60°  to  the  horizontal,  and  are  drawn  with 
the  30°-60°  triangle  and  T-square,  the  45°  triangle  so  much  used 
in  mechanical  drawing  being  dispensed  with  (Fig.  7). 


PRELIMINARY  DISCUSSION  AND   EXPLANATIONS          11 

All  of  the  figures  given  in  the  text  oan  be  drawn  in  pencil 
with  the  following  tools:  A  drawing  board;  a  T-square;  a 
30°-60°  triangle;  a  pencil  compass;  an  irregular  curve;  and  the 
necessary  paper,  pencil,  and  scale  or  ruler.  To  ink  the  drawings 
requires  the  usual  pens  and  ink. 

7.  Center  Lines  and  Axes. 

An  object  has  three  dimensions,  namely,  length,  width  or 
breadth,  and  height  or  thickness.  In  mechanical  drawing  two 
of  these  dimensions  show  in  any  one  view,  but  it  requires 
a  second  view  to  give  the  third  dimension.  In  isometric  draw- 
ing three  dimensions  are  given  in  one  view. 

In  laying  out  a  mechanical  drawing  it  is  the  usual  practice 
to  work  to  some  reference  line.  This  line  is  usually  a  center  line, 
and  is  either  horizontal  or  vertical.  When  two  center  lines  are 
used,  they  are  drawn  at  right  angles  one  to  the  other.  This 
method  is  also  used  in  isometric  drawing. 

Fig.  8  is  an  isometric  drawing  of  three  planes,  a-b-c-d  and 
e-f-g—h  being  vertical  planes  and  i-j-k-L  a  horizontal  plane.  A 
pah-  of  center  lines  are  show^n  drawn  on  each  plane,  the  lines 
5-5  and  6-6  being  on  the  horizontal  plane  and  the  lines  3-3, 
4-4, 1-1,  and  2-2  being  on  the  vertical  planes.  They  are  showrn 
in  the  conventional  manner  at  A,  B,  and  C,  respectively.  All 
of  these  center  lines,  regardless  of  the  plane  in  which  they  lie, 
would  be  shown  in  mechanical  drawing,  as  illustrated  at  D. 

The  three  planes  shown  are  those  most  usually  assumed 
in  drawing,  and  it  is  important  that  the  reader  note  the  char- 
acteristics of  the  three  sets  of  lines,  as  these  lines  determine 
the  plane  of  the  drawing.  The  lines  shown  at  A  are  at  30° 
with  the  horizontal,  are  drawn  with  the  T-square  and  30°  triangle 
(the  30°  angle  of  the  30°-60°  triangle),  and  are  characteristic 
center  lines  for  use  when  drawing  on  a  horizontal  plane.  The 
lines  shown  at  B  are  drawn,  one  vertical  and  one  at  30°  with 
the  horizontal  (with  the  T-square  and  30°  triangle),  and  are 
characteristic  center  lines  for  use  when  drawing  on  what  may 
be  termed  a  left-hand  vertical  plane.  The  center  lines  shown 
at  C  are  drawn,  one  vertical  and  one  at  an  angle  of  30°  with  the 


12 


ISOMETRIC  DRAWING 


horizontal,  and  are  characteristic  center  lines  for  use  when 
drawing  on  what  may  be  termed  a  right-hand  vertical  plane. 
When  drawing  in  any  one  of  the  above  three  planes  the  draw- 
ing is  limited  to  two  dimensions  only — plane  figures;  to  repre- 
sent objects  with  three  dimensions — solids — a  third  principal 
line  of  reference  is  used,  called  an  axis.  The  dashed  lines 
shown  at  A,  B,  and  C  of  Fig.  8  represent  such  lines,  and,  as 


I 


FIG.  8. 


in  the  cases  A,  B,  and  C  mentioned  above  in  connection  with 
characteristic  center  lines,  are  characteristic  axes  for  isometric 
drawings. 

8.  Flexibility. 

The  center  lines  and  axes  just  described  are  the  basis  or  base 
lines  for  all  isometric  drawing,  and  as  long  as  the  relation 
between  the  three  lines  as  shown  in  Fig.  8  is  maintained  they 
may  be  drawn  at  will.  For  practical  purposes  the  direction 
of  the  lines  is  determined  by  -the  drawing  tools  used,  the  T-square 
and  triangle.  The  four  usual  arrangements  are  shown  at  a, 
b,  c,  and  d  of  Fig.  9. 

Being  thus  able  to  select  a  number  of  directions  for  drawing 


PRELIMINARY  DISCUSSION   A^D   EXPLANATIONS          13 


the  axis  of  a  drawing,  isometric  drawing  permits  an  object  to 
be  shown  in  a  number  of  different  positions,  as  illustrated  at 


FIG.  9. 

A,  B,  C,  and  D,  Fig.  9,  and  at  5-1,  B-2,  5-3,  5-4,  5-5,  Fig. 
39. 


FIG.  10. 


In  addition  to  being  able  to  show  an  object  in  different 
positions,  sections  may  be  shown  in  isometric  drawings  the  same 
as  in  ordinary  mechanical  drawing. 


14 


ISOMETRIC   DRAWING 


PLATE  No.  3. 


PRELIMINARY    DISCUSSION   AND  EXPLANATIONS  15 

Plate  3  illustrates  the  flexibility  of  the  art:  Fig.  1  is  a  two- 
view  mechanical  drawing  of  a  loose  pulley,  the  face  view  show- 
ing a  half  section;  Fig.  2  is  an  isometric  drawing  of  the  pulley, 
showing  the  same  section  removed  as  in  Fig.  1 ;  and  Figs.  2,  3, 
and  4  show  the  pulley  in  different  positions. 

Fig.  10  is  a  three-view  mechanical  drawing  of  an  indicator 
cock  or  valve,  and  an  isometric  drawing  of  the  same  valve. 
The  drawings  show  a  section  of  the  valve  removed  to  show 
the  interior. 

Plate  3  and  Fig.  10,  together  with  the  other  illustrations 
of  the  text,  serve  to  demonstrate  the  flexibility  of  the  art. 


f 


CHAPTER  II 
THE  DRAWING  OF  PLANE  FIGURES 

9.  To  Draw  a  Square. 

Fig.  11  illustrates  a  square  drawn  in  different  positions, 
drawing  A  being  a  mechanical  drawing  and  drawings  B,  C,  and 
D  isometric  drawings.  Drawing  B  represents  the  square  as 
lying  on  the  horizontal  plane;  and  drawings  C  and  D  as  lying 
on  vertical  planes. 

To  construct  the  square  (consider  drawing  £),  draw  the 
center  lines  5-5  and  6-6  with  the  T-square  and  30°  triangle, 

each  line  being  at  30°  with 
the  horizontal.  Next,  as- 
suming the  square  to  be  V 
on  a  side  and  working  from 
the  intersection  of  the  center 
lines,  o,  lay  off,  each  way 
from  the  point  o,  on  each 
center  line,  a  distance  of  \n ', 
or  one-half  of  the  length  of 
a  side  of  the  square,  and  lo- 
cate the  points  6,  6  and  5,  5. 

Lastly,  draw  through  each  of  the  two  points  on  each  center  line 
a  line  parallel  to  the  other  center  line;  these  lines  will  meet 
and  will  form  the  required  figure,  a-b-c-d,  as  shown. 

Drawings  C  and  D  are  drawn  in  like  manner,  the  only  dif- 
ference being  in  the  direction  of  the  center  lines,  which  may, 
however,  be  drawn,  as  before,  with  the  T-square  and  30°-60° 
triangle. 

10.  To  Draw  a  Hexagon. 

Fig.  12  represents  the  drawing  of  a  hexagon,  drawing  A 
being  a  mechanical  drawing,  and  drawings  B-I,  B-2,  C,  and  D 

16 


FIG.  11. 


THE    DRAWING    OF    PLANE   FIGURES 


17 


isometric  drawings.  Of  the  isometric  drawings,  B-l  and  B-2 
are  on  horizontal  planes  and  drawings  C  and  D  on  vertical 
planes. 

In  mechanical  drawing  the  drawings  are  always  drawn 
square  with  the  center  lines,  as  shown  at  A,  and  not  as  shown 
at  E-}  this  custom  prevails  because  of  the  better  appearing 
drawings  produced  and  because  of  the  greater  convenience  and 
speed  secured  when  executing  the  drawing.  This  method  of 
drawing  things  square  with  the  center  lines  is  followed  in  iso- 
metric drawing. 

To  construct  the  hexagon  (consider  drawing  5-2),  first 
draw  the  center  lines  5-5  and  6-6  at  the  angle  shown.  Now 


FIG.  12. 

a  hexagon  has  two  so-called  diameters  or  dimensions,  namely, 
the  distance  between  opposite  sides  or  flats,  as  distance  7-7, 
drawing  A,  and  the  distance  between  opposite  corners,  the 
diagonal  distance,  as  distance  a-d,  drawing  A.  Second,  work- 
ing each  way  from  the  intersection  of  the  two  center  lines,  o, 
lay  off  one-half  of  the  diagonal  distance  on  one  center  line, 
and  one-half  of  the  flat  distance  or  dimension  on  the  other 
center  line.  This  gives  the  points  a,  dy  5,  and  5,  respectively, 
Third,  draw  lines  through  the  points  obtained  by  laying  off 
the  flat  diameter  of  the  hexagon,  the  points  5  and  5,  and  on 
each  line  lay  off,  each  way  from  the  point  through  which  the 
line  is  drawn,  one-half  of  the  length  of  a  side  of  the  hexagon. 
This  gives  the  points  6,  c,  e,  and  /.  Fourth,  and  lastly,  connect 


18 


ISOMETRIC   DRAWING 


the  six  points  now  located,  as  shown,  giving  the  required  figure. 
[See  also  Article  13,  (d)  and  (e).] 

11.  To  Draw  an  Octagon. 

Fig.  13  shows  an  octagon — a  mechanical  drawing  of  the 
figure  at  A,  an  isometric  drawing  on  a  horizontal  plane  at  B, 
and  isometric  drawings  on  vertical  planes  at  C  and  D. 

The  figure  may  be  constructed  in  two  ways : 
First  method  (consider  drawing  C). 

Draw  the  center  lines  1-1  and  2-2.  On  these  center  lines 
construct  the  "  square  of  the  octagon,"  b-d-f-h,  as  shown, 

and  as  explained  in  Article 
9.  Next,  working  from  the 
intersection  of  the  center 
lines,  o,  lay  off  each  way 
on  each  center  line,  one- 
half  of  the  diagonal  distance 
or  diameter  of  the  octagon. 
This  gives  the  points  a,  c, 
e,  and  g.  Lastly,  join  the 
eight  points,  as  showrn,  and 
form  the  octagon. 
Second  method  (consider  drawing  D). 

This  method  is  by  referring  all  of  the  points  to  the  center 
lines.  In  drawing  A,  consider  points  a,  6,  c,  d,  e,  /,  g,  and  h 
projected  (perpendicularly)  onto  the  center  lines,  giving  on 
center  line  c-g  the  points  c,  x,  o,  y,  and  g,  and  on  line  a-e  the 
points  a,  m,  o,  n,  and  e.  To  draw  the  isometric  drawing  D, 
first  draw  the  center  lines  as  shown,  and,  working  from  point 
o,  lay  off  on  each  the  corresponding  above-mentioned  projected 
points ;  that  is,  on  line  a-e,  lay  off  points  a,  m,  o,  n,  and  e,  and 
on  line  c-g  points  c,  x,  o,  y  and  g.  Second,  through  the  points 
x  and  y  on  line  c-g  draw  indefinite  lines  (such  as  lines  b-x-d 
and  h-y-f)  parallel  to  center  line  a-e.  Third,  draw  indefinite 
lines  through  the  points  m  and  n  on  center  line  a-e  parallel 
to  center  line  c-g.  These  two  lines  will  intersect  the  pair  first 
drawn  and  will  locate  points  b,  d,  f,  and  h.  The  points  a,  c,  e, 


FIG.  13. 


THE   DRAWING   OF   PLAXE    FIGURES  19 

and  g,  being  on  the  center  lines,  are  fixed,  and,  to  finish  the 
figure,  connect  the  eight  points  found,  as  shown. 

When  an  octagon  on  a  horizontal  plane  lies  within  a  cir- 
cumscribing   circle,  the   construction  of    the    figure  is  much 
simplified  thereby.     In  such  a 
case,   Fig.   14,  first  draw  the 
center  lines  5-5  and  6-6.    Sec- 
ond, draw  the  circumscribing 
circle  (the  construction  of    a 
circle  is  given  in  Article  13). 
Third,  draw  a  horizontal  and 
a    vertical    line   through    the  „ 

intersection  of  the  center  lines, 

point  o.  Fourth,  and  lastly,  join  the  eight  points  in  which  the 
center  lines  and  the  last  drawn  two  lines  cut  the  circumference 
of  the  circle.1  It  is  obvious  that  a  similar  construction  can 
be  applied  when  drawing  on  a  vertical  plane 

12.  To  Draw  Any  Polygon. 

Fig.  15  represents  the  construction  of  a  ten-sided  figure  and 
of  a  fifteen-sided  figure,  and  is  typical  of  any  polygon.  The 
method  shown  is  what  may  be  called  "  plotting,"  and  is  based 
on  the  reference  of  all  points  to  the  center  lines.  In  any  plane 
figure  each  and  every  point  has  two  dimensions,  so  to  speak. 
For  example,  a  point  is  so  far  from  each  of  the  two  center  lines; 
in  drawing  A-l,  point  c  is  c-5  (or  4-0)  distance  from  the  vertical 
center  line,  and  c-4  (or  5-o)  distance  from  the  horizontal  center 
line.  Xow  if  these  distances  are  known,  they  may  be  laid  off 
on  the  center  lines,  a  line  drawn  through  the  point  on  one  center 
line  parallel  to  the  other  center  line,  and  the  point  located  by 
the  intersection  of  the  lines  drawn. 

To  construct  the  fifteen-sided  figure : 

In  drawing  A-2,  project  all  of  the  points  onto  the  vertical 
center  line  (giving  points  a,  15,  16,  17,  o,  18,  19,  20,  and  21), 
then  all  onto  the  horizontal  center  line  (giving  points  1,  2,  3,  4, 
5,  6,  7,  o,  8,  9,  10,  11,  12,  13,  and  14).  Second,  draw  the  iso- 

1  The  isometric  drawing  of  a  circle  is  an  ellipse,  but  is  spoken  of  as  a 
"  circle." 


20 


ISOMETRIC   DRAWING 


metric  center  lines  a-21  and  1-14  (drawing  B-2),  and,  working 
from  their  point  of  intersection,  o,  lay  off  the  points  a,  15,  16, 
17,  o,  18,  19,  20,  and  21  on  the  line  a-21  and  the  points  1,  2,  3, 
4,  5,  6,  7,  o,  8,  9, 10, 11, 12, 13,  and  14  on  the  line  1-14.  Third, 
draw  lines  through  the  points  on  line  a-21  parallel  to  line  1-14, 
then  lines  through  the  points  on  line  1-14  parallel  to  line  a-21. 
The  intersection  of  the  two  lines  drawn  through  the  point  on  each 
of  the  two  center  lines  obtained  (at  the  start)  by  the  projection 
of  any  corner  onto  the  center  lines,  locates  the  point  in  question, 
and  the  series  of  lines  the  several  points  a,  6,  c,  d,  etc.  Lastly, 
join  the  points  as  shown. 


a-l 


FIG.  15. 


In  cases  where  the  necessary  dimensions  for  executing  the 
drawing  cannot,  readijy  be  obtained  from  the  object,  it  is  neces- 
sary to  first  construct  a  mechanical  drawing  of  the  part  or  detail 
in  question,  to  draw  the  center  lines  of  the  figure,  and  to  pro- 
ject the  point  or  points  on  these  lines  (as  in  drawings  A-l  and 
A-2)',  then  take  up  the  isometric  drawing,  using  the  distances 
or  dimensions  thus  obtained  for  its  construction. 

13.  To  Draw  a  Circle. 

Figs.  16 'and  17  are  drawings  of  a  circle,  and  represent  two 
methods  of  construction. 
(a)  First  method.  ^ 

Fig.  16,  illustrates  the  mechanical  drawing  of  a  circle  (draw- 


THE    DRAWING    OF    PLANE   FIGURES 


21 


ing  A)  and  the  isometric  drawing  of  a  circle  (drawings  B,  C  and 
D),  drawing  B  being  on  a  horizontal  plane  and  drawings  C 
and  D  on  vertical  planes. 

To  construct  the  figure  (consider  drawing  B),  first  draw  the 
center  lines  a-b  and  c-d,  each  at  30°  with  the  horizontal.  Second, 
working  from  the  intersection  of  the  two  center  lines,  o,  lay  off 
on  each  center  line,  each  way  from  point  o,  a  distance  equal 
to  the  radius  of  the  circle.  This  gives  points  a,  6,  c,  and  d. 
Third,  through  each  of  the  two  points  on  each  center  line  draw 
a  line  parallel  to  the  other  center  line.  These  four  lines  will 
form  a  diamond-shaped  figure  (a  parallelogram),  1-2-3-4. 


FIG.  16. 

Fourth,  with  the  point  2  as  a  center  and  the  distance  from  the 
point  to  the  middle  of  the  opposite  side  of  the  parallelogram, 
distance  2-c,  as  a  radius,  describe  the  arc'c-6.  •  Fifth,  with  the 
point  4  as  a  center  and  a  radius  equal  to  the  distance  from  the 
point  to  the  middle  of  the  opposite  side  of  the  parallelogram 
as  a  radius,  distance  4-J,  describe  the  arc  a-d.  Sixth,  draw 
the  diagonal  of  the  parallelogram,  the  line  1-3,  and  where 
this  line  intersects  the  lines  2-c  and  4-d,  the  points  x  and  y, 
take  new  centers  and,  with  a  radius  equal  to  the  distance  from 
either  point  to  the  middle  of  the  nearest  sides  of  the  parallelogram 
such  as  distances  x-c  or  y-d,  draw  the  arcs  a-c  and  b-d,  com- 
pleting the  ellipse  a-d-b-c — the  isometric  representation  of  the 
circle. 


22 


ISOMETRIC   DRAWING 


The    ellipse  or  "  circle  "  in  drawing  C  or  D,  the  plane  of 
which  is  vertical,  is  drawn  in  a  manner  similar  to  that  just 
described.    The   method   just   explained   is   an   approximate 
method. 
(6)  Second  method. 

Fig.  17  illustrates  a  second  method  of  constructing  an  iso- 
metric drawing  of  a  circle.  In  the  figure,  drawing  A  is  a  mechan- 
ical drawing  and  drawing  B  an  isometric  drawing.  The  method 
shown  is  similar  to  that  employed  in  Fig.  15  and  described  in 
Article  12,  and  is  what  has  been  termed  plotting. 

To  construct  the  figure,  first  draw  the  mechanical  drawing 
of  the  circle  (A),  divide  the  circumference  into  any  number 


FIG.  17. 

of  points,  project  these  points  onto  the  center  lines,  then  take 
up  the  isometric  drawing.  In  this  (drawing  B),  the  center 
lines  are  drawn;  the  points  of  division,  V,  a,  6,  c,  o}  etc.,  obtained 
by  the  projection  of  the  points  of  division  of  the  circle  onto  the 
center  lines  (drawing  A),  laid  off;  lines  drawn  through  the 
points  of  division  as  showrn;  the  points  4,  5,  6,  etc.,  located  by 
the  intersection  of  the  lines;  and  the  closed  curve  V,  4,  5,  6, 
etc.,  obtained  by  drawing  a  smooth  curve  through  the  points 
found — all  as  suggested  and  shown  by  the  figure. 

The  method  just  described  is  an  exact  method. 
(c)  Error  cf  the  first  method. 

The  two  methods  given  for  making  an  isometric  drawing 
of  a  circle  are  shown  applied  in  Fig.  18,  the  circle  (so  called) 
a-b-c-d  being  drawn  by  the  first,  or  approximate,  method,  and 


THE  DRAWING   OF  PLANE   FIGURES 


23 


the  circle  a-e-b-f-c-g-d-h  drawn  by  the  second,   or  exact, 
method. 

An  inspection  of  the  figure  shows  that  the  approximate 
method  gives  a  representation  which  is  shorter  and  wider  than 


FIG.  18. 

that  obtained  by  the  exact  method.  The  approximate  method, 
being  the  easier  of  application,  is  the  one  used  practically,  and 
because  of  its  two  errors  sometimes  leads  to  slight  comph* ca- 
tions in  the  construction  of  drawings;  for  example,  when  the 
circle  joins  or  fits  into  or  about  some  other  figure  or  part,  as 
when  drawing  a  sphere,  a  circumscribing  or  inscribed  circle,  etc. 

Fig.  19  illustrates  a  circle  drawn  by  the  two  methods  already 
given,  the  dotted  curve  being  drawn  by  the  approximate  method 
and  the  full-line  curve  by  the 
exact  method;  also,  the  draw- 
ing of  a  hexagon,  in  two  posi- 
tions, about  the  true  circle 
(Article  10).  The  particular 
points  to  be  noted  in  this 
figure  are  that  in  either  hexa- 
gon the  length  of  each  of  the 
two  sides  which  are  parallel 

with  one  of  the  center  lines  (a-b  and  d-e  or  h-4  and  k-T)  is  the 
true  length  of  a  side  of  the  hexagon,  and  that  each  of  these 
two  lines  (a-b  and  d-e,  or  h-i  and  k-l)  is  symmetrical  with  the 
center  line  (being  divided  into  two,  a-b  and  d-e  at  H,  and  h-i 
and  k-l  at  V). 

Fig.  20  illustrates  a  circle  drawn  by  the  approximate  method, 
and  an  inscribed  (the  dashed-line  figure)  and  a  circumscribed 


FIG.  19. 


24  ISOMETRIC   DRAWING 

(the  full-line  figure)  hexagon.  The  dotted  hexagon  A'-B'-C-D' 
-Ef-F  is  a  correct  drawing  of  the  circumscribed  hexagon 
without  reference  to  the  circle  and  shows,  at  the  corners  A',  B', 
D',  and  E'}  the  error  of  a  hexagon  drawn  with  reference  to  a 
circle  drawn  by  the  approximate  method. 

The  particular  feature  to  note  in  this  figure  is  that  in  the 
hexagon  the  two  sides  (A-B  and  D-E  or  a-b  and  d-e,  which  are 
drawn  parallel  with  the  center  line  7-7,  are  unsymme  trie  al  with 
the  center  line  H-H,  being  longer  on  one  side  (H-B  and  H-E 
or  h-b  and  h-e)  than  on  the  other  (A-H  and  H-D  or  a-h  and 
h-d). 

The  convenience  of  the  approximate  method  for  drawing 
a  circle,  and  the  large  number 
of  circles  and  circular  arcs 
always  to  be  drawn  more 
than  outweigh  the  errors 
(such  as  described  above)  in- 
troduced by  its  adoption  and 
application.  In  cases  where 
a  discrepancy  shows  up,  it  pIG  20. 

will   be   but   slight,  and   it  is 

customary  and  an  easy  matter  to  adapt  the  lines  so  as  to  make 
the  conditions  fit. 

(d)  To  draw  an  inscribed  hexagon. 

To  draw  a  hexagon  within  a  circle  (Fig.  20),  first  draw 
the  circle  by  the  approximate  method  [Article  13  (a)].  Where 
the  center  line  V—V  cuts  the  circle,  points  c  and  /,  locates 
two  points ,  of  the  hexagon.  Second,  working  from,  point  o, 
lay  off  on  the  center  line  H-H,  each  way  from  o,  one-half  of 
the  distance  between  sides  of  the  hexagon,  the  length  o-h,  and 
draw  through  each  of  the  two  points  thus  obtained  a  line  parallel 
to  the  center  line  7-7.  Where  these  lines  cut  the  circle,  points 
a,  b,  d,  and  e,  locates  four  points  of  the  hexagon.  Third,  join 
the  six  points  found,  and  the  hexagon  a-b-c-d-e-f  is  obtained. 

(e)  To  draw  a  circumscribed  hexagon. 

To  draw  a  circumscribed  hexagon  (Fig.  20),  first  draw  the 
isometric  representation  of  the  circle  by  the  approximate 


THE    DRAWING    OF    PLANE    FIGURES 


25 


method.  Second,  working  from  the  point  o,  lay  off  on  the  center 
line  V-V,  each  way  from  o,  one-half  of  the  distance  between 
corners  of  the  hexagon  (the  lengths  o-C  and  o-F).  This  locates 
two  points  (C  and  F)  of  the  hexagon.  Third,  through  each 
of  the  points  H,  in  which  the  center  line  H-H  intersects  the  ellipse 
H-X-Y-H,  etc .,  draw  a  line  parallel  to  center  line  V-V.  Fourth, 
from  the  points  C  and  F  draw  lines,  each  way,  tangent  to  the 
circle  (points  X,  Y}  M,  and  N)  intersecting  the  lines  drawn 
through  the  points  H  parallel  to  line  V-V.  The  intersection 
of  these  lines  locates  the  remaining  four  corners  of  the  hexagon, 
and  the  construction  completes  the  drawing  of  the  figure. 
(/)  To  draw  a  series  of  uniform  circles  the  centers  of  which  lie  in 
the  same  straight  line  and  plane. 

Fig.  21  illustrates  a  number  of  uniform  circles  with  centers 
in  a  common  straight  line,  drawing  A  being  a  mechanical 
drawing  and  drawing  B  an  isometric  drawing. 


FIG.  21. 

To  construct  the  isometric  drawing,  first  consider  one  circle 
only,  as,  for  example,  the  circle  r-l-s-1  of  drawing  Af  and  draw 
the  isometric  representation  of  this  circle  by  the  approximate 
method  [Article  13  (a)],  as  shown  in  drawing  B  by  the  parallelo- 
gram a-b-c-d}  the  radii  /,  g,  h,  and  i,  and  the  ellipse  r-l-s-1. 
Second,  extend  the  center  line  r-s,  the  lines  a-b  and  d-c}  and 
through  the  points  x  and  Y  draw  lines  parallel  to  the  above 
lines,  all  as  shown  by  the  line  s-s2  and  the  dashed  lines  b-m, 
c-p,  x-n  and  Y-O,  respectively.  Third,  lay  off  on  the  line  d-p 
the  distances  d-di,  and  d^d2  equal  to  the  length  e,  the  distance 
between  centers  of  the  circles;  and,  with  a  radius  equal  to 
radius  h  and  the  points  dlt  d2  as  centers,  describe  the  arcs  2-Sj 


26 


ISOMETRIC    DRAWING 


and  3-s2  (parallel  to  the  arc  1-s).  Fourth,  locate  the  points 
bi  and  b2  in  like  manner  and,  with  these  points  as  centers  and 
a  radius  equal  to  radius  g,  draw  the  arcs  rx-2  and  r2-3  (parallel 
to  the  arc  r-1).  Fifth,  lay  off  on  the  line  x-n  the  distances 
x-xx  and  Xj-x-j  equal  to  the  length  e,  the  distance  between  cen- 
ters of  the  circles  and,  with  the  points  xx  and  x2  as  centers  and 
a  radius  equal  to  radius/,  draw  the  arcs  2-r,  and  3-r2.  Sixth, 
and  lastly,  locate  the  points  YJ  and  Y2  in  a  similar  manner  and, 
with  these  as  centers  and  a  radius  equal  to  the  radius  i,  draw 
the  arcs  2-s1;  and  3-s2,  completing  the  figure. 

A  considerable  amount  of  labor  of  construction  is  eliminated 
by  keeping  the  above  scheme  in  mind,  and  it  is  offered  to  call 
attention  to  the  fact  that  there  are  many  such  "  short  cuts  " 
which  will  become  apparent  after  some  little  practice  in  the  art, 
and  which  should  always  be  taken  advantage  of. 

14.  To  Draw  an  Ellipse. 

Fig.  22  illustrates  the  drawing  of  an  ellipse.  A  is  the  mechan- 
ical drawing,  and  B  the  isometric  drawing.  The  isometric 
drawing  is  shown  on  a  vertical  plane. 


FIG.  22. 

To  draw  the  figure,  first  divide  the  ellipse  as  drawn  at  A 
into  a  number  of  points,  as  points  a,  &,  c,  etc.;  then  project 
the  points  onto  the  center  lines  as  shown  by  the  points  1,  2,  3, 
4,  etc.  Second,  draw  the  center  lines  H-H  and  V-V  of  draw- 
ing B,  and  on  them  lay  off  the  corresponding  divisions  on  the 
center  lines  of  drawing  A,  points  1,  2,  3,  4,  etc.  Third,  through 
the  divisions  on  each  center  line  draw  lines  parallel  to  the  other 


THE    DRAWING,  OF    PLANE   FIGURES 


27 


center  line.  The  point  in  which  the  lines  through  the  two  points 
on  the  center  lines  (one  on  each)  representing  the  projection 
of  any  one  point  intersect,  will  locate  that  particular  point, 
and  the  series  of  lines  the  several  points  a,  b,  c,  etc.  Fourth, 
and  lastly,  through  the  points  thus  obtained  and  the  points 
H,  H  and  V,  V,  the  ends  of  the  axes  of  the  ellipse,  draw  the 
curve  H,  a,  b,  c,  etc.,  the  isometric  drawing  of  the  ellipse. 

15.  To  Draw  an  Hyperbola. 

Fig.  23  illustrates  an  hyperbola.  Drawing  A  is  the  mechan- 
ical, and  drawing  B  the  isometric  drawing.  The  feature  of 
this  figure  is  that  it  has  but  one  center  line  (line  1-e)  and  intro- 
duces the  use  of  a  second  line  of  reference  which  may  be  called 
a  base  line  (line  5-12). 


FIG.  23.  FIG.  24. 

To  draw  the  figure,  first  divide  the  curve  into  a  number  of 
points,  as  points  a,  b,  c,  etc.,  of  drawing  A;  then  project  each 
point  into  the  center  line  and  onto  the  base  line,  thus  obtaining 
the  points  1,  2,  3,  etc.  Second,  draw  the  center  line  1-e  and  the 
base  line  5-12  of  drawing  B,  and  on  them  lay  off  the  points 
1,  2,  3,  etc.  Third,  draw  lines  through  each  of  these  points 
as  shown  and  locate  the  points  a,  6,  c,  etc.  Fourth,  through 
the  points  thus  located  draw  the  curve  a,  b,  c,  etc.,  the  isometric 
drawing  of  the  hyperbola. 

16.  To  Draw  a  Parabola. 

Fig.  24  illustrates  two  drawings  of  a  parabola,  drawing  A 
being  a  mechanical  drawing  and  drawing  B  an  isometric  drawing. 


28  ISOMETRIC  DRAWING 

The  construction  is  the  same  as  described  in  Article  15, 
and  is  clearly  shown  by  the  figure. 

17.  To  Draw  an  Undulating  Figure. 

It  will  have  been  noted  that  most  of  the  figures  given  thus 
far  are  shown  drawn  on  the  horizontal  plane,  Figs.  17,  18, 19,  20, 
and  21,  for  example,  and  that  the  last  three,  Figs.  22,  23  and  24, 
are  drawn  on  vertical  planes.  This  is  done  to  acquaint  the 
reader  with  the  flexibility  of  the  art  (Article  8),  and  to  illustrate 
the  procedure  on  the  two  planes.  To  further  illustrate  the 
choice  of  position  or  plane  in  which  to  draw,  Fig.  25  is  offered. 
It  illustrates  the  drawing  of  an  undulating  figure  made  up 


of  semicircles,  and  shows  the  drawing  on  what  may  be  termed 
an  oblique  plane  the  center  lines  for  which  agree  with  those 
illustrated  in  Fig.  9  at  d. 

To  draw  the  figure,  draw  the  horizontal  line  H-H  and  on 
it  lay  off  the  points  a,  b,  c,  and  d,  a  distance  apart  equal  to  the 
distance  between  centers  of  the  circular  arcs  as  shown  in  drawing 
A.  Second,  through  each  point  draw  a  center  line  V-V  at  60° 
with  the  horizontal.  Third,  on  each  pair  of  center  lines,  such 
as  H-H  and  V-a-V,  lay  out  the  necessary  lining  and  construct  a 
semicircle  as  described  in  Article  13  (a),  and,  as  shown  by  the 
figure,  the  series  of  semicircles  will  form  the  required  figure. 

18.  To  Draw  Any  Figure  Composed  of  Straight  Lines  and  Cir- 
cular Arcs. 

Fig.  26  illustrates  the  drawing  of  a  figure  made  up  by  a 
combination  of  straight  lines  and  circular  arcs.  The  iso- 


THE    DRAWING    OF    PLANE  FIGURES 


29 


metric  drawing  B  is  on  a  vertical  plane,  and  the  construction 
very  similar  to  that  described  in  Article  17. 

To  construct  the  figure,  first  draw  the  center  line  H-H  at 
30°  with  the  horizontal,  and  on  it  lay  off  the  center  points 
a,  6,  c,  and  d,  corresponding  to  the  center  points  a,  b,  c,  and  d 
of  drawing  A.  Second,  through  each  point  draw  a  center  line 
V-V,  and  on  each  pair  of  center  lines  thus  formed  proceed  with 
the  lay-out  for  drawing  a  circle  by  the  approximate  method 
(Article  13),  and  obtain  the  centers  and  radii  necessary  to 
describe  the  arcs  of  the  figure — all  as  illustrated.  Lastly, 
connect  the  circular  arcs  with  straight  lines  as  shown. 

Combinations  of  straight  lines  and  circular  arcs  are  very 
frequent  in  drawing  and  it  is  important  that  the  draughtsman 


FIG.  26. 

know  how  to  treat  them.  Sometimes  they  are  in  such  a  form 
that  a  beginner  does  not  recognize  or  think  of  them  as  such. 
One  of  the  examples  most  frequently  met,  with  is  the  represent- 
ing of  round  corners  of  figures  and  objects. 

Fig.  27  illustrates  a  square  with  rounded  corners.  It  will 
be  noted  from  an  inspection  of  the  figure  that  the  arcs  at  the 
corners  are  circular  arcs,  and  that  they  may  be  continued 
to  form  complete  circles  and  the  figures  to  come  under  a  con- 
struction as  given  for  Fig.  26. 

To  construct  the  isometric  drawing  B,  first  draw  the  center 
lines  H-H  and  V-V,  and  construct  the  square  W-X-Y-Z 
(Article  9).  Second,  consider  the  lower  left-hand  corner  of 
the  figure,  W,  and  from  the  corner  lay  off,  each  way,  a  distance 
equal  to  radius  R,  as  lengths  W-f  and  W-e'}  through  the  points 


30 


ISOMETRIC    DRAWING 


thus  obtained,  points  /  and  e,  draw  the  center  lines  /-/  and  e-e. 
Third,  working  to  the  center  lines  just  found,  use  the  approx- 
imate method  for  drawing  a  circle  (Article  13),  and  locate  the 
center  point  o  and  the  radius  r,  and  describe  the  full-line  arc 
f-e,  that  portion  of  the  ellipse  f-e-f-e  forming  the  rounded 
corner  in  question.  Fourth,  in  a  similar  manner  draw  in  the 
full-line  curve  a-b  at  corner  X,  as  shown  by  the  drawing. 

The  curves  at  corners  Y  and  Z  may  be  obtained  in  a  similar 
manner,  though  with  a  little  less  work.  That  is,  now  that  the 
scheme  is  known,  in  applying  the  method  for  drawing  a  circle, 
only  that  portion  of  the  entire  construction  used  for  the  drawing 


FIG.  27. 

of  a  circle  needed  to  locate  the  center  point  and  the  necessary 
radius  need  be  drawn,  the  construction  being  clearly  shown  in 
the  figure. 

19.  The  Proper  Arrangement  of  All  Drawings  with  Reference  to 
the  Center  Lines,  and  the  Manner  of  Laying  Off  Dimen- 
sions. 

It  will  have  been  noticed  that  all  of  the  constructions  given 
thus  far  begin  with  the  drawing  of  the  two  center  lines,  and  that 
the  figures  then  drawn  are  drawn  square  with  the  center  lines. 
Also,  that  the  dimensions  are  all  laid  off  on  the  center  lines, 
or  on  lines  parallel  to  the  center  lines.  This  is  the  correct 
practice  in  isometric  drawing,  and  is  but  in  strict  accordance 
with  the  usual  and  accepted  practice  in  ordinary  mechanical 
drawing. 


THE    DRAWING, OF    PLANE  FIGURES 


31 


Fig.  28  shows  at  drawings  A  and  ^.-1  the  usual  placing  of 
a  hexagon  with  reference  to  the  center  lines;  drawing  A-2 
shows  an  unusual  arrangement.  When  such  an  arrangement 
is  to  be  drawn  in  isometric,  the  corners  of  the  hexagon  must 
be  referred  to  the  center  lines  and  the  points  located  by  plotting, 
as  directed  in  Article  12,  and  as  shown  by  drawing  B-2. 

It  may  be  well  to  note  the  four  right  angles  formed  by  the 
center  lines  in  drawings  A-2  and  B-2.  The  angle  7-0-1  of 
drawing  A-2  is  shown  as  7-0-1 
of  drawing  B-2  (note  that 
this  angle  as  drawn  is  more 
than  a  right  angle,  but  in 
isometric  drawing  is  used  as 
and  called  a  right  angle), 
and  the  angle  7-0-6  of  draw- 
ing A-2  is  shown  at  B-2  as 
the  angle  7-0-6  (note  that 
this  angle  as  drawn  is  less 
than  90°,  but  is  used  as  and 
called  a  right  angle).  The 
other  two  angles  are  readily 
noted  in  the  figure. 

In  mechanical  drawings  the  two  dimensions  of  plane  figures 
are  always  either  vertical  or  horizontal;  in  isometric  drawing 
one  dimension  is  sometimes  vertical  and  sometimes  horizontal 
(never  one  horizontal  and  the  other  vertical),  and  when  it  is 
so  the  other  dimension  is  always  at  an  angle  to  the  horizontal 
or  vertical  (see  Article  8),  the  arrangement  depending  upon 
the  arrangement  of  the  center  lines  of  the  figure  in  question. 

It  should  be  remembered,  therefore,  to  always  lay  off  dimen- 
sions parallel  with  the  center  lines  of  the  figure  drawn,  and  when 
measuring  an  isometric  drawing  to  scale  it  in  directions  parallel 
with  the  center  lines. 


A-2 


FIG.  28. 


CHAPTER  III 
THE  DRAWING   OF   SOLIDS 

20.  Preparatory. 

The  student  is  cautioned  not  to  attempt  the  reading  of  this 
chapter  without  first  reading  Chapter  II  and  mastering,  in  so 
far  as  possible,  the  principles  and  methods  there  set  forth. 
The  drawing  of  solids  is  based  on  the  drawing  of  plane  figures, 
and  the  only  new  feature  introduced  in  this  chapter  is  the 
drawing  on  different  planes,  not  as  set  forth  in  Article  8  and  as 
illustrated  by  the  figures  of  Chapter  II,  exactly,  but  the  drawing 
on  all  of  the  planes  mentioned,  possibly  in  the  same  illustration, 
with  a  definite  relation  as  to  position  to  all  of  the  other  planes. 

If  one  has  a  thorough  knowledge  of  the  methods  given  in 
Chapter  II,  the  only  difficulty  likely  to  be  encountered  when 
making  isometric  drawings  of  solids  is  to  get  the  drawing  of  any 
particular  feature  of  the  object  drawn  on  the  correct  plane.  This 
is  the  one  difficulty  which  is  of  serious  moment  to  the  beginner, 
and  requires  some  little  experience  and  practice  to  eliminate. 
To  reduce  such  trouble  to  a  minimum  the  student  should  care- 
fully consider  the  part  in  question,  note  the  plane  (horizontal 
or  vertical)  on  which  it  lies,  then  note  the  center  lines  of  the 
plane  of  his  drawing.  If  the  center  lines  are  drawn  as  set  forth 
in  Article  7,  the  correct  plane  can  always  be  established. 

A  second,  minor,  difficulty  often  encountered  is  to  get  the 
correct  position  of  the  plane  on  which  to  draw.  This  is  a  matter 
of  dimension  and  lay-out,  and  the  difficulty  can  only  be  eliminated 
by  the  student's  keeping  in  mind  that  all  dimensions  must  be 
laid  out  along  lines  which  are  parallel  writh  the  center  lines 
or  axis  of  the  figure  or  drawing. 

Coming  now  to  the  drawing  of  solids,  the  drawings  have 
three  dimensions,  and  use  is  made  of  the  third  of  the  three  lines 

32 


THE   DRAWING  OF    SOLIDS 


33 


mentioned  in  Article  7  (the  axis)  and  illustrated  in  Fig.  8  at 
.4.,  Bj  and  C,  and  Fig.  9  at  a,  6,  c,  and  d.  These  three  lines  are 
the  basis  of  all  of  the  constructions  which  follow. 

21.  To  Draw  a  Rectangular  Block. 

Fig.  29  is  an  illustration  of  a  rectangular  block,  drawing  A 
being  a  mechanical  drawing  and  drawings  B,  B-l,  and  B-2 
isometric  drawings.  The  isometric  drawings  show  the  block 
in  three  different  positions,  also  three  different  constructions. 
All  of  the  constructions  are  simple,  but  should  be  considered. 
They  are : 


-h- 

i  - 

» 

1.  To  construct  drawing  B,  first  draw   the  center  lines 
H-H  and  V-V,  and  on  them  construct  the  rectangle  1-2-3-4 
as  explained  in  Article  9,  the  size  of  the  rectangle  to  agree  with 
the  dimensions  of  the  top  face  of  the  block.     Second,  draw^ 
the  line  X-Y  (the  axis  for  the  center  lines  H-H  and  V-V, 
Article  7)  and  on  it  lay  off  a  length  o-o'  equal  to  the  thickness 
of  the  block.    Third,  through  the  point  o'  draw  the  center  lines 
h-h  and  v-v,  and  working  to  these  construct  the  rectangle 
5-6-7-8.    Fourth,  and  lastly,  join  the  points  1  and  5,  2  and  6, 
etc.,  completing  the  figure  as  shown. 

2.  To  construct  drawing  B—l,  first  draw  the  center  lines  H-H 
and  V-V  and  on  them  construct  the  face  1-2-3-4.    Second, 
draw  the  axis  for  the  center  lines  just  used,  line  X—Y,  and  on 
it  lay  off  the  length  of  the  block  and  locate  the  point  ol '.    Third, 
through  the  point  o'  draw  center  lines,  and  working  to  them 


34 


ISOMETRIC    DRAWING 


construct  the  face  5-6-7-8.     Fourth,  join  the  corners  of  two 
bases  as  shown. 

3.  To  construct  drawing  B-2,  first  draw  the  face  1-2-3-4 
as  in  the  second  construction.  Second,  through  the  points 
1,  4,  and  3,  draw  lines  parallel  to  the  axis  of  the  block,  and  on 
them  lay  off  lengths  equal  to  the  length  of  the  block.  This 
locates  points  5,  8,  and  7.  Third,  join  the  points  5  and  8,  and 
7  and  8. 

22.  To  Draw  a  Pyramid  of  Blocks. 

Fig.  30  illustrates  a  number  of  square  blocks,  piled  one  upon 
the  other  in  such  a  manner  as  to  keep  the  pile  symmetrical. 


FIG.  30. 

To  construct  the  isometric  drawing  (B),  first  draw  the  center 
lines  a-a  and  b-b,  and  on  them  construct  the  square  1-2-3-4, 
as  explained  in  Article  9.  Second,  from  the  corners  1,  3,  and  4, 
drop  vertical  lines,  and  on  the  line  through  the  point  4  lay  off 
a  length  4-4'  equal  to  the  thickness  of  the  block.  Third,  through 
the  point  thus  located  (point  4')  draw  the  lines  4 '-3'  and  4'-l' 
parallel  to  the  center  lines  a-a  and  b-b,  respectively.  Fourth, 
through  the  intersection  of  the  center  lines,  point  o,  draw  the 
axis  X-Y,  and  on  it  lay  off  a  length  equal  to  the  thickness  of 
the  top  or  smallest  block.  Fifth,  through  the  point  thus  located, 
point  o',  draw  the  center  lines  c-c  and  d-d',  working  to  them 
construct  the  square  5-G-7-8  and  finish  the  drawing  of  the  out- 


THE    DRAWING    OF  SOLIDS 


35 


line  of  the  second  block,  all  in  a  manner  similar  to  the  drawing 

of  the  first  block.     Sixth,  establish  the  plane  of  the  top  of  the 

third  block  by  dropping  down 

from  point  o'  to  o"  a  distance 

equal  to  the  thickness  of  the 

second  block  and  drawing  the 

center  lines  e-e  and  f-f,  and 

construct    the   outline   of  the 

third  block  as  shown.   Seventh, 

proceed    in  a  similar  manner 

for    the    construction    of    the 

fourth  block,  and  complete  the 

figure. 

23.  To  Draw  an  Hexagonal  Prism. 

Fig.  31  illustrates  the  con-  FIG.  31. 

struction  of  an  hexagonal  prism. 

To  construct  the  figure,  first  draw  the  center  lines  a-a  and  b-b, 
and  on  these  construct  the  hexagon  1-2-3-4-5-6,  as  explained 
in  Article  10.  Second,  draw  the  axis  of  the  figure,  the  line 
X-Y,  and  on  it  lay  off  a  length  o-o'  equal  to  the  length  of  the 

prism.  Third,  through  the 
point  o'  draw  the  center  lines 
c-c  and  d-d,  and  working  to 
them  construct  the  hexagon 
l'_2'-3'-4'-5'-6'.  Fourth, 
join  the  comers  of  the  two 
bases  as  shown,  completing 
the  figure. 

24.  To   Draw  an  Hexagonal 
Pyramid. 

Fig.  32  illustrates  the  con- 
struction of  an  hexagonal 
pyramid. 

To  construct  the  figure,  first  draw  the  center  lines  a-a  and 
6-6,  and  working  to  them  construct  the  hexagon  1-2-3-4-5-6 
as  directed  in  Article  10.  Second,  draw  the  axis  X-Y,  and 


FIG.  32. 


36 


ISOMETRIC  DRAWING 


from  the  point  o  lay  off  a  length  o-o'  equal  to  the  height  of  the 
pyramid.    Third,  join  each  corner  of  the  hexagon  with  the 
point  o'. 
25.  To  Draw  Any  Rectangular  Solid  which  is  of  Uniform  or 

Similar  Section. 

Fig.  33  is  an  illustration  of  a  clamp  block,  and  is,  like  the 
objects  illustrated  in  Figs.  29  and  31,  uniform  in  section,  and 
is  drawn  in  a  similar  manner. 

To  construct  the  figure,  first  draw  the  center  lines  a-a  and 
b-b.  Second,  working  from  the  point  o,  lay  off,  each  way,  the 

lengths  o-4, 4-3,  etc.,  correspond- 
ing to  the  widths  of  the  object 
as  defined  in  drawing  A .  Third, 
working  from  point  o,  lay  off 
the  lengths  o-r  and  o-s,  as 
shown,  corresponding  to  the 
thickness  of  the  block .  Fourth, 
through  the  points  on  each 
center  line  draw  lines  parallel 
to  the  other  center  line;  the 
intersection  of  these  two  sets  of 
lines  will  locate  all  points  of  the 
end  face  of  the  object,  which 
may  be  drawn  by  joining  the 
points  as  shown.  Fifth,  draw 
the  axis  X-Y  and  on  it  lay  off,  from  point  o,  a  length  o-o' 
equal  to  the  length  of  the  block.  Sixth,  through  the  point  o' 
draw  the  center  lines  c-c  and  d-d,  and  working  to  them  draw 
the  outline  of  the  rear  face  of  the  block.  Seventh,  connect  the 
two  faces  by  joining  the  corners,  and  complete  the  figure,  as 
shown. 

Attention  is  called  to  the  similarity  of  the  above  construc- 
tion of  the  visible  end  face  to  that  given  for  drawing  any  polygon, 
Article  12.  It  is  as  much  "  plotting  "  as  the  method  there 
described.  Also,  note  that  the  center  lines  used  are  not,  exactly, 
what  are  usually  termed  center  lines.  The  point  to  be  noted  is 
that  the  method  or  scheme  for  executing  the  construction  of  all 


FIG.  33. 


THE   DRAWING  OF  SOLIDS 


37 


figures  is  similar,  and  that  center  lines  may  be  used  as  base  or 
reference  lines. 

From  Figs.  29,  31,  and  33  it  may  be  taken  as  a  general 
construction  for  all  objects  which  are  uniform  in  section,  to 
first  construct  the  two  ends  or  bases,  then  join  the  bases 
properly,  forming  the  sides  and  completing  the  figure. 

Fig.  34  illustrates  two  objects  which  taper  from  one  end  to 
the  other,  objects  of  which  a  section  at  any  point  is  similar  to  a 
section  at  any  and  all  other  points.  Drawing  A  is  a  mechanical 
drawing  of  a  crank  blank,  drawing  B  its  isometric  representation, 
and  drawing  C  an  isometric  drawing  of  a  steel  key. 


FIG.  34. 

The  method  for  constructing  such  figures  is  similar  to  that 
used  when  the  section  of  the  object  drawn  is  uniform;  that  is, 
to  first  draw  the  two  ends  (end  sections),  then  join  the  two  as 
may  be  necessary  to  finish  the  figure. 

For  example,  to  draw  the  steel  key  shown  at  (7,  first  draw 
the  end  section  1-2-3-4;  second,  the  end  section  5-6-7-8; 
and,  third,  join  the  sections  as  shown. 

The  illustration  of  the  crank  is  offered  to  show  a  very  dif- 
ferent type  of  model  from  those  given  thus  far,  namely,  objects 
of  a  rectangular  nature;  but  it  will  be  noted  that  the  treatment 
or  method  of  construction  of  the  drawing  is  the  same.  To 
construct  drawing  B,  first  establish  the  three  sets  of  center 
lines  of  the  large  end,  as  when  drawing- the  pyramid  of  blocks 


38 


ISOMETRIC   DRAWING 


(Article  22),  and  working  to  them  construct  the  three  ellipses 
(Article  13)  shown.  Second,  proceeding  in  a  similar  manner, 
construct  the  three  ellipses  of  the  small  end  of  the  figure.  And, 
third,  join  up  the  two  ends  with  tangent  lines,  as  shown. 

26.  To  Draw  Any  Rectangular  Solid  of  Variable  Section. 

Fig.  35  is  an  illustration  of  a  draughtsman's  pencil-pointing 
pad,  the  handle  of  which  varies  in  width.  The  construction 
of  the  drawing  of  this  part  of  the  object  demonstrates  a  method 

of  procedure  applicable  to  the 
representation  of  any  rect- 
angular object  of  variable 
section. 

The  rectangular  part  of 
the  figure  (drawing  B)  is 
drawn  in  a  manner  similar  to 
that  illustrated  in  Fig.  30  and 
described  in  Article  22.  To 
construct  the  drawing  of  the 
handle,  first  draw  the  center 
or  base  line,  m-n.  Second, 
divide  this  line  into  a  num- 
ber of  parts  (such  as  by  a 
FIG.  35.  point  every  |"  or  |",  or  by 

taking  points  at  places  where 

the  section  of  the  object  drawn  changes)  by  marking  off 
points  such  as  points  1,  2,  3,  etc.  Third,  through  each 
point  draw  a  line  at  right  angles  (so  called  in  isometric 
drawing)  to  the  line  m-n  (note  that  the  line  through  any 
point  is  but  a  second  center  line),  and  on  each  line  lay 
off,  each  way  from  the  point  on  the  line  m-n,  a  length  equal 
to  one-half  of  the  width  of  the  handle  at  that  point,  obtain- 
ing the  points  a,  6,  c,  d,  etc.  Fourth,  through  the  points 
thus  located  draw  the  curve,  the  outline  of  the  handle,  as 
shown.  To  draw  the  bottom  curve,  the  line  defining  the 
thickness  of  the  handle,  draw  vertical  lines  j-j'9  i-4r ,  etc.,  througn 
the  points  /,  i,  etc.,  and  on  each  line  Jay  off  a  length  equal  to 


THE   DRAWING    OF    SOLIDS 


39 


the  thickness  of  the  handle,  locating  points  /',  i' ',  etc.,  and  draw 
through  these  points  as  shown. 

The  above  example  happens  to  be  such  that  the  curves 
drawn  (on  the  top  plane)  are  symmetrical  with  the  center  line 
m-n :  should  the  case  be  different,  a  base  line  may  be  used  for 
reference  and  from  it  the  construction  can  be  laid  out,  but  the 
method  is  similar  to  that  just  described. 

27.  To  Draw  a  Cylinder. 

The  drawing  of  a  circle  is  given  in  Article  13,  and  the  draw- 
ing of  a  solid  of  uniform  section  in  Article  25,  the  drawing  of  a 
cylinder  is  based  on  these  two  constructions. 


5-2 


FIG.  36. 

Fig.  36  is  an  illustration  of  a  right  cylinder,  drawing  A  being 
a  mechanical  drawing  and  drawings  B-l  and  B-2  isometric 
drawings.  • 

To  construct  drawing  B-l,  first  drawr  the  center  lines  a-b 
and  c-d,  and  in  accordance  with  Article  13  construct  the  ellipse 
of  the  upper  base.  Second,  draw  the  axis  of  the  cylinder,  the 
line  X-Yj  and  on  it  lay  off  the  length  o-of  equal  to  the  length 
of  the  cylinder.  Third,  at  the  point  o'  establish  the  plane  of 
the  lower  base  by  drawing  the  center  lines  af-b'  and  c'-d'  and 
construct  the  ellipse  a'-c'-b'-d' .  Fourth,  draw  vertical  lines 
tangent  to  the  two  bases,  completing  the  figure. 

To  construct  drawing  B-2,  first  draw  the  center  lines  a-b 
and  c-d,  and  draw  the  ellipse  representing  the  near  end  of  the 


40 


ISOMETRIC   DRAWING 


FIG.  37. 


cylinder  in  accordance  with  the  above  reference  and  as  shown 
by  the  centers  1,  2,  3,  and  4,  and  the  radii  R,  S,  r,  and  s.  Second, 
shift  the  center  points  1,  2,  3,  and  4  along  the  lines  1-1',  2-2', 
etc.  (parallel  to  the  axisX-F),  a  distance  equal  to  the  length 

of  the  cylinder,  and,  with  the 
new  position  of  the  center 
points,  points  1',  2',  3',  and 
4',  as  centers  and  the  same 
radii  as  used  to  draw  the 
front  end  of  the  cylinder; 
draw  the  rear  end,  as  shown. 
Third,  draw  lines  tangent  to 
the  two  bases. 

28.  To  Draw  a  Cone. 

Fig.  37  illustrates  the  con- 
struction of  a  cone. 
To  construct  drawing  B,  first  draw  the  center  lines  a-b  and 
c-d,  and  working  to  them  describe  the  ellipse  a-c-b-d  (Article 
13)  of  the  base.  Second,  through  the  point  o,  draw  the  axis 
of  the  cone,  the  line  X-Y,  and  on  it  lay  off  a  length  o-o'  equal 
to  the  altitude  or  height  of  the  cone.  Third,  from  the  point  o' 
draw  lines  tangent  to  the  base. 

29.  To  Draw  a  Solid  Made 

Up  of  Circular  Arcs  and 

Straight  Lines. 

Very  often  an  object 
will  have  a  number  of 
curves  which  are  circular 
arcs.  When  such  is  the 
case,  the  construction  is 
similar  to  that  described 
in  Article  18. 

Fig.  38  illustrates  the 
isometric  drawing  of  two 
objects  the  lines  of  which  are  either  straight  lines  or  circular 
arcs.  Drawing  M  represents  a  core  box,  and  drawing  N  a  cap 
for  a  bearing. 


FIG.  38. 


THE  DRAWING    OF   SOLIDS  41 

To  draw  the  circular  arc  showing  at  the  bottom  of  the  core 
box  (arc  a-d),  consider  the  arc  as  extended  to  complete  the 
circle  of  which  it  is  a  part;  then  lay  out  the  construction  for 
drawing  a  circle  (Article  13),  locate  the  center  point  and  the 
radius  for  describing  that  portion  of  the  ellipse  covered  by  the 
arc  in  question  (in  this  case,  one-fourth  of  the  circumference), 
and  draw  in  the  required  curve. 

The  drawing  of  the  bearing  cap  is  offered  as  a  second  example 
of  the  application  of  the  above  method  of  drawing  parts  of 
circles,  and  the  construction,  which  is  clearly  shown  in  the 
figure,  should  be  carefully  noted. 

Attention  is  called  to  the  arc  at  the  bottom  of  the  figure; 
this  arc  is  drawn  by  dropping  the  point  m  to  m'  a  length  equal 
to  the  length  of  the  object,  and,  with  this  new  point  as  a  center, 
and  a  radius  s,  the  same  radius  used  to  draw  the  corresponding 
arc  at  the  top,  drawing  it  in,  as  shown. 

30.  To  Draw  a  Ring,  Rectangular  in  Section. 

Fig.  39  illustrates  the  drawing  of  a  ring  which  is  rectangular 
in  section.  Drawing  A  is  a  mechanical  drawing  and  drawings 
B-l,  B-2,  B-3,  B-4,  and  B-5  are  isometric  drawings.  The 
several  isometric  drawings  are  given  to  illustrate  the  choice 
of  view  or  position  of  the  object  open  to  the  draughtsmen. 

The  figure  should  be  compared  with  Fig.  9,  and  the  similarity 
of  position  of  the  center  lines  and  axis  of  the  various  drawings 
noted.  For  example,  the  position  B-l  corresponds  to  position 
d  of  Fig.  9,  B-3  to  6,  and  position  B-o  to  position  c.  The  posi- 
tions B-2  and  B-4  have  no  corresponding  position  shown  in 
Fig.  9,  but  it  will  be  noted  that  the  relation  of  the  lines  used  as 
center  lines  and  axis  is  the  same  as  in  all  isometric  drawing, 
that  is,  adjacent  lines  forming  an  angle  of  60°,  as  shown. 

The  construction  of  the  several  drawings  is  identical,  and  is 
illustrated  in  drawing  B-l.  To  construct  this  drawing,  first 
draw  the  center  lines  a-b  and  c-d,  and  working  to  them  lay  off, 
each  way  from  the  point  o,  a  length  equal  to  the  radius  of  the 
inside  of  the  ring,  locating  the  points  1,  2,  3,  and  4.  Second, 
through  these  points  draw  the  figure  e-f-g-h,  and  within  this 


42 


ISOMETRIC   DRAWING 


the  ellipse  1-2-3-4,  all  as  directed  for  drawing  the  representa- 
tion of  a  circle  in  isometric,  and  as  shown.  Third,  working 
to  the  same  center  lines,  since  the  two  circles  of  the  end  face 
are  in  the  same  plane,  proceed  in  a  similar  manner  and  construct 
the  ellipse  5-6-7-8.  Fourth,  draw  such  portions  of  the  right 
end  face  of  the  ring  as  are  visible,  and  finish  the  figure  by  draw- 
ing the  two  outside  lines  (top  and  bottom)  tangent  to  the  two 
bases. 

The  lines  of  the  drawing  show  every  line  of  the  construction. 
Attention  is  again  called  to  the  short  method  employed  for 


FIG.  39. 

drawing  the  arcs  of  the  ellipses  showing  in  the  rear  base  or  end 
of  the  ring.  For  example,  consider  the  outside  curve  at  the 
rear,  the  line  w'-S'-G'-/;  this  curve  is  parallel  to  the  curve 
i/>-5-6-2  of  the  front  face.  To  draw  the  arc  at  the  rear,  first 
draw  through  the  points  5  and  6  the  guide  lines  5-5'  and  6-6' 
parallel  to  the  axis  (line  X—Y)  of  the  ring.  Second,  draw  a 
similar  line  through  the  point  i,  and  on  it  lay  off  a  length  i-4r 
equal  to  the  thickness  or  length  of  the  ring,  and,  with  the  point 
thus  located,  the  point  i',  as  a  center  and  a  radius  H'  equal  to 
radius  R,  describe  the  arc  5'-6'.  Third,  in  like  manner  shift 


THE  DRAWING    OF    SOLIDS 


43 


the  center  point  r  to  r',  and  s  to  s',  and,  with  the  new  position 
of  the  points  as  centers  and  the  same  radius  as  used  for  the 
corresponding  arc  of  the  front  face  of  the  ring,  describe  the 
arcs  o'-w'  and  G'-z',  thus  finishing  the  arc  entire. 

31.  To  Draw  a  Circular  Disc  with  Holes  in  it. 

Fig.  40  is  an  illustration  of  a  disc  with  three  equally  spaced 
countersunk  holes  in  it. 

To  construct  the  figure,  the  disc  may  be  considered  as  a  short 
cylinder  and  its  outline  drawn  accordingly  (Article  27),  the 


FIG.  40. 

center  of  the  holes  located  by  reference  to  the  center  lines  of 
the  top  face  of  the  disc,  the  planes  of  the  circles  representing 
the  outline  of  the  countersunk  hole  located  as  shown  in  Fig. 
30  and  explained  in  Article  22,  and  the  ellipse  defining  the  holes 
drawn  as  explained  in  Article  13. 

The  new  feature  introduced  by  this  figure  is  the  location 
and  drawing  of  the  countersunk  holes.  On  the  contrary,  how- 
ever, the  so-called  "  new  feature  "  is  not  new,  as  the  construc- 
tion is  only  the  application  of  methods  already  known.  The 
feature  is  an  ever-recurrent  one,  and  it  is  important  that  the 
student  understand  the  method  of  procedure. 

Since  it  is  correct  practice  to  draw  things  square  with  the 
center  lines  when  drawing  objects  such  as  the  disc  shown, 
square  as  many  features  with  the  center  lines  as  possible.  For 


44 


ISOMETRIC   DRAWING 


example,  if  there  should  be  but  a  single  hole  in  the  object, 
construct  the  drawing  with  the  center  of  the  hole  on  one  of  the 
center  lines;  if  the  object  has  two  holes  either  90°  or  180°  apart, 
see  that  they  are  located  on  the  center  lines;  if  the  object  has 
four  holes  equally  spaced,  place  the  centers  on  the  center  lines, 
etc.  When  there  is  an  unequal  number  of  holes,  as  in  the  present 
case  of  three,  place  one  of  the  holes  on  one  of  the  center  lines, 
and,  by  plotting,  referring  the  centers  to  the  center  lines,  locate 
the  centers  for  the  other  two  holes  as  shown. 

It  must  always  be  borne  in  mind  that  an  isometric  drawing 
is  not  measured  or  laid  out  like  a  mechanical  drawing,  but 
that  all  dimensions  must  be  laid  out  or  taken  in  some  one  of 
three  directions,  that  is,  parallel  to  either  center  line  or  to  the  axis. 


FIG.  41, 

32.  To  Draw  a  Stepped  Pulley. 

Fig.  41  is  an  illustration  of  a  three-stepped  cone  pulley. 

To  construct  the  figure  (drawing  B),  first  draw  the  center 
lines  of  the  plane  of  the  top  face,  the  lines  a-b  and  c-d,  and 
working  to  them  draw  the  outline  of  the  hole  through  the  center 
(Article  13;  also  see  Fig.  42).  Second,  working  to  the  same 
set  of  center  lines,  in  similar  manner  draw  the  ellipse  5-6-7-8. 
Third,  drop  the  three  centers  used  to  draw  the  arc  z-6-5-2/ 


THE   DRAWING    OF   SOLIDS 


45 


a  distance  equal  to  the  dimension  T  and,  with  the  same  radii 
used  to  draw  the  above  curve,  draw  the  arc  £'-6'-5',  all  as 
directed  for  drawing  the  cylinder  (Article  27)  and  as  explained 
in  connection  with  the  construction  of  the  drawing  of  the  ring 
(Article  30). 

The  remainder  of  the  construction  is  similar  to  that  already 
given,  the  procedure  being  to  drop  down  the  axis  X-Y  dis- 
tances T,  S  and  E,  locate  the  points  o',  o"  and-o'",  establish 
new  planes  at  these  points,  and  working  to  the  center  lines 
drawn  draw  in  the  several  ellipses  and  complete  the  figure  as 
shown. 

33.  To  Take  Out  a  Section. 

In  mechanical  drawing  it  is  customary  when  removing  a 
section  to  remove  some  portion  limited  by  the  center  lines. 
For  example,  in  the  case  of  the  stepped  pulley,  Fig.  41,  if  a 
half  section  is  to  be  shown,  the  quarter  assumed  to  be  removed 
would  not  be  such  a  one  as  is 
included  in  the  angle  w-o-z 
(drawing  A),  but  one  such  as 
is  included  in  the  angle  c-a-b. 
This  practice  holds,  also,  in 
isometric  drawing,  and  a  sec- 
tion such  as  would  show  in 
the  angle  u-o-y  of  drawing  5, 
Fig.  41,  is  never  given,  the 
correct  method  being  illustrated 
by  Fig.  42. 

Fig.  42  illustrates  the  usual  procedure  for  drawing  an  object 
with  a  section  removed.  The  lines  are  all  shown,  and,  in  the 
light  of  what  has  been  given  thus  far,  the  figure  should  prove 
self  explanatory. 

When  executing  such  as  the  above,  two  methods  may  be 
followed:  (1)  To  first  make  the  construction  for  the  entire 
figure,  then  remove  the  section;  (2)  To  make  the  construc- 
tion for  only  that  portion  of  the  object  which  is  to  show  in  the 
figure.  The  first  construction  is  the  safer  for  the  beginner, 
and  should  be  followed  at  first;  after  some  experience  the 


FIG.  42. 


46 


ISOMETRIC   DRAWING 


work  may  be  shortened  in  a  number  of  ways  which  will  then 
be  apparent. 

34.  To  Draw  an  Eccentric. 

Fig.  43  is  an  illustration  of  a  small  eccentric  blank.  The 
dimensions  are  given  on  the  mechanical  drawing  (.4)  that  the 
student  may  make  the  exact  construction,  should  he  care  to  do 
so.  The  figure  does  not  introduce  anything  new,  but  is  given 
as  an  example  illustrating  the  inaccuracy  of  the  method  used 
for  drawing  the  isometric  representation  of  a  circle. 


FIG.  43. 


The  error  of  the  method  is  discussed  in  paragraph  (c)  of 
Article  13,  and  is  illustrated  at  the  points  M  and  N  of  drawing 
B,  Fig.  43.  If  the  method  used  were  exact,  the  ellipse  a-b-c-d 
and  the  ellipse  1-2-3^  would  be  tangent  at  the  point  M 
instead  of  intersecting;  also,  the  slight  discrepancy  at  point  N 
would  be  eliminated.  However,  the  drawing  is  but  an  illus- 
tration, and  no  harm  is  done  when  the  curves  are  made  to 
look  right  by  joining  them  as  shown. 

The  student  will,  doubtless,  encounter  many  similar  con- 
ditions in  his  work.  When  such  cases  do  occur,  adjust  the 


THE   DRAWING  OF   SOLIDS 


47 


curves  to  match  in  such  a  way  as  to  make  the  drawing  appear 
natural. 

To  construct  drawing  B,  first  consider  the  outer  rim  of  the 
eccentric  as  a  ring,  and  make  the  construction  as  directed  in 
Article  30.  Second,  consider  the  hub,  or  center,  as  a  cylinder, 
and  make  the  construction  as  in  Article  27.  Third,  locate 
the  points  o'  by  dimension,  draw  the  ellipses  1-2-3-4  and 
5-6-7-8  as  a  guide,  then  adjust  the  curves  to  meet  the  ellipse 
a-b-c-d,  as  mentioned  above. 

The^^ure  shows  such  lines  as  will  suggest  the  several  steps 
necessa^r  f or  the  construction,  showing  the  particular  radii 
and  centers  necessary  to  be  shifted  to  draw  the  curves  at  the 
back,  or  rear,  of  the  figure. 


FIG.  44. 

35.  To  Draw  an  Hexagonal  Nut. 

In  all  machine  drawing  there  are  always  a  number  of  bolt 
heads  and  nuts  to  represent.  Fig.  44  is  given  as  illustrating  a 
typical  construction,  the  figure  being  the  representation  of  an 
hexagonal  nut. 

To  construct  the  figure,  first  draw  the  center  lines  H-H  and 
V-Vj  and  working  to  them  construct  the  hexagon  1-2-3-4-5-6 
as  directed  in  Article  10.  Second,  at  each  corner  point  of  the 
hexagon  erect  a  vertical  line,  and  on  each  line  lay  off  a  length 
equal  to  the  length  of  a  corner  of  the  nut,  locating  the  points 
1',  2',  3',  4',  5',  and  6'.  Third,  bisect  each  side  of  the  hexagon 
1-2-3-4-5-6,  at  each  middle  point  erect  a  vertical  line,  and  on 
it  lay  off  a  length  equal  to  the  greatest  width  of  a  side  of  the  nut, 


48 


ISOMETRIC   DRAWING 


locating  the  points  7',  8',  9',  10',  11',  and  12'  and  giving,  with 
the  two  points  already  located,  three  points  in  the  curve  at  the 
top  of  each  side  face  of  the  nut.  Fourth,  draw  a  curved  line 
(using  the  irregular  curve)  through  the  points  thus  located,  as 
shown.  Fifth,  draw  the  axis  X-Y  through  the  point  o,  and  on 
it  lay  off  a  length  o-o'  equal  to  the  thickness  of  the  nut.  Sixth, 
through  the  point  0'  draw  the  center  lines  a-b  and  c-d,  and 
working  to  them  draw  the  two  circles  showing  in  the  top  face 
of  the  nut,  in  accordance  with  Article  13,  completing  the  figure. 


FIG.  45. 

36.  To  Draw  a  Hollow  Cylinder  with  a  Section  Removed. 

Fig.  45  represents  a  hollow  cylinder  with  a  section  removed 
and  is  offered  to  further  illustrate  the  taking  of  sections  in 
isometric  drawing. 

To  construct  drawing  B,  proceed  as  directed  in  Article  27 
and  as  suggested  by  the  lines  of  'the  figure,  and  draw  the  outline 
of  the  cylinder;  then  consider  the  hole  through  the  cylinder 
as  a  second  cylinder,  and  draw  its  outline  in  a  similar  manner. 
To  take  out  the  section,  pass  a  plane  e-f-g-h  through  the  cylinder 
and  on  it  draw  the  section  of  the  cylinder,  as  shown;  then  remove 
the  section  between  the  plane  of  the  front  end  and  the  section 
plane  included  between  the  planes  l-l'-o'-o  and  0-o'-2'-2, 
the  construction  being  evident  from  the  illustration. 


THE  DRAWING    OF  SOLIDS 


49 


37.  To  Draw  Any  Solid  of  Revolution. 

Figs.  46  and  47  are  illustrations  of  certain  objects  with  no 
particular  name,  but  typical  of  any  object  of  revolution,  that 


FIG.  46. 

is,  any  object  a  section  at  right  angles  to  the  axis  of  which  is 
circle. 


FIG.  47. 


To  draw  such  an  object,  pass  a  series  of  transverse  sec- 
tional planes  through  it,  draw  the  sections  thus  taken,  then 


50  ISOMETRIC    DRAWING 

draw  the  outline  of  the  figure  by  drawing  lines  tangent  to  the 
sections. 

In  the  further  discussion,  sections  used  as  above  will  be  called 
"  guide  sections." 

To  construct  Fig.  46,  first  draw  the  axis  X-Y  and  on  it 
locate  the  points  o,  o'  and  o",  according  to  dimensions  as  taken 
from  drawing  A  or  from  the  object.  Second,  at  each  of  the 
three  points  draw  center  lines,  and  in  accordance  with  Article 
13  (taking  the  diameters  of  the  circles  from  drawing  A)  draw 


FIG.  48. 

the  three  ellipses,  as  shown.  Third,  draw  tangent  lines  to  the 
three  ellipses,  finishing  the  figure. 

The  construction  of  Fig.  47  is  similar  to  that  of  Fig.  46, 
the  difference  being  that  three  intermediate  guide  planes  are 
used  instead  of  but  one,  and  the  outline  of  the  figure  is  a  curve 
instead  of  a  straight  line,  as  in  Fig.  46. 

The  use  of  guide  sections  is  not  limited  to  the  construction 
of  representations  of  solids  of  revolution,  but  may  be  used  to 
advantage  when  drawing  many  other  types  of  figures,  as,  for 
example,  in  Fig.  48,  where  the  application  is  self  evident. 


THE  DRAWING  OF   SOLIDS 


51 


38.  To  Draw  a  Ring,  Circular  in  Section. 

Fig.  49  illustrates  a  mechanical  (A)  and  an  isometric  (B) 
drawing  of  a  ring  which  is  circular  in  section. 

To  execute  drawing  B,  first  pass  a  number  of  radial  planes 
through  the  ring,  as  indicated  in  drawing  A,  cutting  the  ring 
in  a  number  of  sections.  Second,  refer  the  center  lines  of  each 
section  of  drawing  A  to  the  center  lines  of  the  figure  (as  indi- 
cated for  section  number  12),  and  by  plotting  establish  their 
position  in  drawing  B.  Third,  on  each  pair  of  center  lines  con- 
struct a  parallelogram,  and  within  each  parallelogram  describe 


FIG.  49. 

an  ellipse.    Fourth,  draw  lines  tangent  to  the  series  of  ellipses, 
all  as  suggested  and  shown  by  the  figure. 

39.  To  Draw  Screw  Threads. 

To  actually  construct  a  correct  representation  of  a  screw 
thread  is  a  somewhat  difficult  thing  to  do  and  consumes  a  con- 
siderable amount  of  time.  In  fact,  such  a  procedure  is  so 
laborious  and  time-consuming  that  in  ordinary  mechanical 
drawing  certain  conventions  are  adopted  to  render  the  matter 
practical.  This  is  also  true  of  isometric  drawing;  for  while 
it  is  possible  to  construct  a  true  representation  of  a  thread,  it 
is  not  worth  wrhile,  as  certain  easily  executed  conventional 
methods  of  representation  serve  very  wrell. 

Fig.  50  illustrates  one  of  the  conventional  representations 
mentioned,  drawing  A  being  a  mechanical  drawing  and  drawing 
B  an  isometric  drawing. 


52 


ISOMETRIC  DRAWING 


To  construct  the  isometric  drawing,  first  consider  the  object 
as  a  cylinder  and  construct  the  outline  of  the  front  and  rear 
bases  and  connect  them  with  tangent  lines  as  directed  in  Article 
27.  Second,  on  the  plane  of  the  front  face  of  the  cylinder 
draw  the  center  lines  H-H  and  V-V  (these  will  be  the  same 
lines  as  used  to  obtain  the  ellipse  of  the  front  face),  and  working 
to  them  lay  out  the  construction  for  the  isometric  representation 
of  a  circle  of  a  diameter  equal  to  the  internal  diameter  of  the 
thread  (Article  13).  Third,  through  the  points  b  and  e  draw 


*1 

m 

- 

FIG.  50. 

the  lines  m-n  and  o-p,  respectively.  Fourth,  beginning  at  the 
point  numbered  1,  lay  off  a  series  of  divisions  on  the  line  X-Y 
equal  to  the  distance  between  the  top  and  bottom  points  of 
the  thread ;  then  with  the  same  radius  as  used  to  draw  the  arc 
b-e,  and  using  each  of  the  points  2,  3,  4,  etc.,  as  centers,  draw 
a  series  of  arcs  parallel  to  arc  b-e  and  terminated  by  the  lines 
m-n  and  o-p.  Fourth,  through  the  center  points  used  to  draw 
the  arcs  b-c  and  d-e  draw  the  lines  r-s  and  t-u,  respectively; 
lay  off  on  each  line  a  series  of  divisions  equal  to  those  laid  off 
on  the  line  X-Y,  and,  with  the  same  radius  as  used  to  draw  the 
arcs  b-c  and  d-e,  using  each  point  as  a  center  and  picking  up 


THE  DRAWING  OF  SOLIDS 


53 


each  of  the  arcs  first  drawn  and  terminated  by  the  lines  m-n 
and  o-p,  continue  the  curves  until  they  disappear. 

Fig.  51  is  an  illustration  of  the  object  illustrated  in  Fig. 
50,  showing  a  section  removed  and  disclosing  the  points  and  roots 
of  the  thread.  The  outline  of  the  figure  and  the  arcs  represent- 
ing the  thread  are  drawrn  as  described  for  the  construction  of 
Fig.  50.  The  new  feature  introduced  by  the  illustration  is 
the  construction  of  the  section  of  the  thread. 

The  construction  of  the  thread  on  either  side  is  identical 
and  is  illustrated  by  the  lines  on  the  left  side.  To  construct 
the  thread,  first  draw  the  two 
guide  lines  on  m-n  and  o-p  a 
distance  apart  (measured  along 
the  center  line  b-c)  equal  to  the 
depth  of  the  thread.  Second,  lay 
off  on  line  m-n  a  series  of  points 
1,  3,  5,  7,  etc.,  a  distance  apart 
equal  to  the  distance  between 
points  of  the  thread  (equal  to  the 
pitch  of  the  thread) .  Third,  bisect 
the  length  1-3,  and  through  the 
middle  point  draw  the  line  r-s 
parallel  to  the  center  line  b-c  and  cutting  the  line  o-p  in  2. 
Fourth,  join  the  points  1  and  2;  then  through  each  point 
of  division  on  the  line  m-n  draw  a  line  parallel  to  the  line 
1-2  and  terminating  at  the  line  o-p.  Fifth,  join  the  points 


FIG.  51. 


FIG.  52. 


2  and  3;   then,  proceeding  as  just  described,  draw  the  parallel 
lines  4-5,  6-7,  etc.,  completing  the  construction. 


54 


ISOMETRIC  DRAWING 


FIG.  53. 


Figs.  50  and  51  illustrate  an  inside  thread.  The  construc- 
tion for  an  outside  thread  is  similar,  and  is  illustrated  by  Fig.  52. 
The  parallel  curves  of  Fig.  52  are,  however,  drawn  at  a  distance 

apart  equal  to  the  pitch  of  the  thread. 
The  matter  of  the  spacing  of  the 
center  points  and  the  resultant  dis- 
tance between  'he  curves  is  a  matter 
of  opinion  with  the  draughtsman;  it 
may  be  equal  to  the  pitch,  to  one- 
half  the  pitch,  or  to  something  else. 
As  a  matter  of  fact,  the  whole 
scheme  is  but  a  representation 
to  suggest  the  thread,  and  any 
combination  that  does  this  will 
answer. 

Square  threads  can  be  illustrated  similarly  to  V-threads, 
as  illustrated  by  Fig.  53. 

Fig.  54  illustrates  three  other  conventions  used  to  represent 
threads,  the  construction  for  each  being  similar  to  that  already 
described.     The  short  curve  of 
No.  3  is  drawn  with  a  shorter 
radius   than   the   middle   por- 
tion of  the  longer  curve,  taken 
optionally    by    the    draughts- 
man. 
40.  To  Draw  a  Sphere. 

To  draw  a  sphere,  execute 
the  isometric  representation  of 

a  circle  of  the  same  diameter  as  the  sphere;  then  take  as  a  radius 
a  length  equal  to  the  semi-major  axis  of  the  ellipse  so  drawn, 
and  draw  a  circle.  The  circle  will  be  the  isometric  representa- 
tion of  the  sphere. 

The  construction  described  above  is  illustrated  in  Fig.  55, 
drawing  A  'being  the  mechanical  drawing  and  drawing  B  the 
isometric  drawing  of  the  same  sphere. 

Fig.  56  illustrates  a  good  example  of  the  application  of  the 
above  construction.  The  figure  illustrates  a  split-pattern  of  a 


No.  1. 


No.  2. 
FIG.  54. 


No.  3. 


THE   DRAWING  OF    SOLIDS 


55 


small   dumb-bell,    drawing    A    being    a   mechanical   drawing, 
drawing  B-l  an  isometric  drawing  showing  the  pattern  together, 


and  drawing  B-2  an  isometric  drawing  showing  the  pattern 
separated. 


FIG.  56. 


Fig.  57  illustrates  a  good  exercise  for  a  beginner.     The  figures 
are  all  isometric  drawings,    drawing  B  representing  a  sphere 


56  ISOMETRIC  DRAWING 

with  a  horizontal  and  two  vertical  (at  right  angles)  great  circles 


FIG.  57. 

on  its  surface.     Drawing  B-l  illustrates  the  sphere  cut  in  twc 

along  the  horizontal  great  circl( 
and  the  two  halves  separated 
Drawing  B-2  illustrates  th< 
sphere  again  cut  in  two  (thi; 
time  along  one  of  the  vertica 
great  circles)  and  the  parti 
separated,  and  drawing  B-l 
shows  it  cut  a  third  time  anc 
the  parts  separated. 

Fig.  58,  illustrating  a  hanc 
wheel,  is  also  an  excellent  type 
of  figure  to  draw  to  test  one'* 
knowledge  of  the  art  and  skil 
FIG.  58.  in  execution. 


CHAPTER  IV 
A  COURSE  IN   ISOMETRIC  DRAWING 

41.  Explanatory. 

The  following  exercises  are  offered  as  covering  practically 
all  of  the  different  constructions  given  in  Chapters  II  and  III, 
and  as  comprising  a  brief  course  in  isometric  drawing.  They 
may  be  followed  exactly,  or  they  may  be  used  as  examples 
only,  and  similar,  original  drawings  made.  It  is  suggested, 
however,  that  the  course  as  outlined  be  followed  out  and  then 
supplemented  as  the  student  or  teacher  may  elect. 

The  exercises  are  planned  to  go  within  a  border  line  which 
is  8"X11"  in  dimensions,  and  a  space  2"X3"  is  reserved  for  the 
title  of  the  sheet.  The  sheets  are  all  alike  in  this  respect,  Plate 
No.  4  showing  the  lay-out  which  is  to  be  followed. 

57 


58 


ISOMETRIC    DRAWING 


PLATE  No.  4. 


A   COURSE   IN,  ISOMETRIC   DRAWING  59 


42.  Sheet  No.  1. 

Sheet  No.  1  is  an  exercise  in  the  drawing  of  some  plane  figures. 
The  sheet  is  to  be  laid  out,  the  figures  located  and  drawn  full 
size  in  accordance  with  the  dimensions  given,  and  the  title 
filled  in  as  shown. 

When  inking-in,  ink  the  border  lines,  the  outlines  of  each 
figure,  and  its  isometric  center  lines.  Omit  all  dimensioning. 

The  finished  sheet  is  to  have  a  margin  \"  wide  all  around 
outside  the  8"Xll"  border  line,  finishing  9"X12"  in  dimen- 
sions. 

The  references  for  the  several  constructions  are  to  be  found 
in  Chapter  II.  For  drawings  1  and  2,  see  Article  9.  For 
drawings  3  and  5,  see  Article  12.  For  drawing  4,  see  Article 

10.  For  drawings  6,  7,  and  8,  see  Article  13.     Drawing  9  is 
but  the  grouping  of  drawings  6,  7,  and  8.     For  drawings  10  and 

11,  see  Article  13  (/).     For  drawings  12  and  16,  see  Article  13 
(d)  and  (e).     For  drawing  14,  see  Article  18.     For  drawing  17, 
see  Article  17. 

To  draw  Fig.  13,  locate  the  six  points  of  a  hexagon  of  1J" 
diagonal  diameter  (Article  10)  and  the  six  points  of  a  hexagon 
of  }"  diagonal  diameter  (the  latter  diagonal  to  be  at  right  angles 
to  the  1J"  diagonal)  and  join  the  points  as  shown. 

To  draw  Fig.  15,  locate  the  six  points  of  a  hexagon  of  1" 
diagonal  diameter  (Article  10);  through  each  of  the  six  points 
thus  located  draw  center  lines  and  working  to  them  (Article 
13)  construct  the  isometric  representation  of  a  circle  of  \" 
diameter. 


60 


ISOMETRIC  DRAWING 


PLATE  No.  5. 


A  COURSE    IN-  ISOMETRIC   DRAWING  61 


43.  Sheet  No.  2. 

Sheet  No.  2  is  an  exercise  in  the  drawing  of  some  straight- 
line  objects. 

The  dimensions  for  the  sheet,  directions  for  finishing,  etc., 
are  the  same  as  for  Sheet  No.  1. 

The  references  for  the  several  constructions  are  to  be  found 
in  Chapter  III. 

Drawing  1  represents  two  blocks  piled  one  upon  the  other; 
drawing  2  represents  a  small  two-drawer  cabinet,  showing  the 
drawers  pulled  part  way  out;  drawing  3  shows  two  rectangular 
frames  pinned  together  at  right  angles  one  to  the  other;  drawing 
5  is  a  representation  of  a  minature  stand;  drawing  4,  an  illus- 
tration of  the  same  stand  stood  upside  down;  drawing  6  shows 
a  frustum  of  an  hexagonal  pyramid ;  and  drawing  7,  an  octagonal 
prism  with  a  section  removed. 

For  drawings  1,  2,  3,  4,  and  5,  see  Articles  21  and  22:,  For 
drawing  Fig.  6,  see  Article  24.  The  construction  of  the  upper 
base  of  the  frustum  is  left  for  the  student  to  figure  out,  the 
upper  base  being  at  30°  with  the  lower  base.  For  drawing  7, 
see  Articles  24,  25,  and  33. 


62 


ISOMETRIC  DRAWING 


PLATE  No.  6. 


A  COURSE    IN   ISOMETRIC  DRAWING  63 


44.  Sheet  No.  3. 

Sheet  No.  3  is  an  exercise  in  the  drawing  of  some  ex- 
amples of  bench  work. 

The  conditions  for  executing  the  sheet  are  the  same  as  for 
Sheet  No.  1. 

The  sheet  is  very  similar  to  Sheet  No.  2,  and  is  offered  as 
giving  additional  practice  in  locating  and  drawing  on  different 
planes. 

Drawing  1  illustrates  a  half -splice;  drawing  2,  a  pinned 
mortise-and-tenon  joint,  showing  the  pieces  ready  to  assemble; 
drawing  4  is  a  keyed  mortise-and-tenon  joint,  Fig.  3  being  the 
key;  drawing  5  shows  a  splayed  splice;  drawing  6  illustrates  a 
plain  dove-tailed  joint;  drawing  7,  a  blind  dove-tailed  joint; 
and  drawing  8,  a  bench-hook. 

The  reference  for  the  entire  sheet  is  to  be  found  in  Chapter 
III,  the  construction  being  based  on  Articles  21,  22,  and  27. 


64 


ISOMETRIC  DRAWING 


PLATE  No.  7. 


A   COURSE  IN  ISOMETRIC   DRAWING  65 


45.  Sheet  No.  4. 

Sheet  No.  4  is  an  exercise  in  the  drawing  of  some  cylindrical 
objects. 

The  conditions  for  executing  the  sheet  are  the  same  as  for 
Sheet  No.  1. 

Drawing  1  is  an  illustration  of  a  core-print;  drawing  2  is  a 
drawing  of  a  circular  nut;  drawing  3  illustrates  a  core  box; 
drawing  4  is  a  special,  combination  nut-and-spacer;  and  drawing 
5  a  face-plate  for  a  wood-turning  lathe. 

The  references  for  the  several  constructions  are  all  to  be 
found  in  Chapter  III,  and  are:  For  Fig.  1,  see  Articles  27  and  37; 
for  Fig.  2,  see  Articles  30  and  39;  for  Fig.  3,  see  Articles  21  and 
29;  for  Fig.  4,  see  Articles  27  and  35;  for  Fig.  5,  see  Articles  27, 
31  and  39. 


66 


ISOMETRIC   DRAWING 


PLATE  No.  8. 


A  COURSE   IN   ISOMETRIC  DRAWING  67 


46.  Sheet  No.  5. 

Sheet  No.  5  is  an  exercise  in  the  drawing  of  some  shop  tools. 

The  sheet  is  offered  as  a  suggestion  only,  and  is  not  to  be 
copied,  no  dimensions  being  given. 

To  execute  the  sheet,  it  is  suggested  that  the  student  obtain 
the  same  or  similar  tools  as  shown  by  the  plate  and,  working 
from  the  tools,  draw  up  an  original  sheet  after  the  manner 
illustrated. 

The  objects  illustrated  are  (1)  a  cold  chisel,  (2)  a  claw  hammer, 
(3)  an  alligator  wrench,  and  (4)  a  plumb  bob. 

All  kinds  of  wrenches,  hammers,  mallets,  screwdrivers,  in 
short,  the  whole  line  of  hand  shop  tools  make  very  good  examples 
to  illustrate. 


68  ISOMETRIC   DRAWING 

47.  Suggested  Sheets. 

The  foregoing  five  sheets  are  given  as  typical  exercises,  and 
for  further  exercise  work  the  student  or  teacher  should  have 
very  little  trouble  in  elaborating  upon  the  course  as  given. 
To  this  end  the  following  suggestions  are  offered :  A  sheet  of 
shop  tools  other  than  those  illustrated  by  Plate  No.  8;  a  sheet 
of  pipe  fittings,  such  as  tees,  ells,  union  couplings,  etc.;  a  sheet 
illustrating  a  globe  or  other  type  valve;  a  sheet  illustrating  a 
simple  building,  or  some  architectural  construction  or  feature; 
or,  in  case  the  above  suggestions  are  too  advanced  or  the  objects 
named  not  obtainable,  books,  blocks,  desks,  cabinets,  and  all 
kinds  of  furniture  and  household  articles,  such  as  spools,  cups, 
glasses,  stove  parts,  etc.,  may  be  used  as  examples. 

48.  Remarks. 

Dimensioning.  Isometric  drawings  are  used  more  for  illus- 
trating than  for  giving  working  directions — working  or  shop 
drawings.  Such  being  the  case,  they  are  not  often  dimensioned. 
As  before  expressed,  however,  they  may  be  dimensioned,  as 
witness  Plates  Nos.  4,  5,  6,  and  7. 

The  dimensions  may  be  given  in  any  way  which  will  make 
them  clear  to  the  reader  of  the  drawing,  but  they  look  best 
when  applied  to  the  drawing  as  on  the  above  named  plates. 

A  reference  to  the  plates  will  show  that  the  dimensions 
apparently  lie  in  the  plane  of  the  part  dimensioned,  and  always 
in  a  direction  parallel  to  one  of  the  three  isometric  directions, 
that  is,  either  parallel  to  one  of  the  two  center  lines  or  to  the 
axis  of  the  drawing.  This  practice  is  recommended. 

Enlargement.  An  isometric  drawing  drawn  full  size  will 
appear  slightly  larger  than  the  object  drawn.  This  feature 
will,  doubtless,  have  been  noted  in  looking  over  the  figures 
of  Chapter  III,  as,  for  example,  Figs.  31,  44,  50,  55,  and  others. 
There  is  a  reason  for  this,  but  it  has  no  connection  with  the 
"  How  "  of  the  art  and  is  purposely  not  discussed  further. 

Distortion.  Some  figures  do  not  appear  natural  when  illus- 
trated by  an  isometric  drawing.  This  is  particularly  noticeable 
in  objects  of  uniform  section  and  of  some  length.  The  eye 
seems  to  instinctively  sense  that  parallel  lines  should  converge 


A  COURSE   IN  ISOMETRIC  DRAWIXG/A. : . . :  : '  '-.8<K  :' 

and,  since,  in  isometric  drawing  they  do  not,  the  drawing 
appears  distorted,  as,  for  example,  Figs.  50  and  52.  This  dis- 
tortion is  so  marked  in  some  representations  that  it  renders  the 
art  unsuited  for  illustrating  that  particular  object.  Distortion 
is  one  of  the  objections  to  isometric  drawing. 

Shading.  "While  the  examples  given  in  the  text  are  not 
shaded,  or  back-lined,  it  is  not  to  be  assumed  that  isometric 
drawings  cannot  be  shaded.  To  shade  an  isometric  drawing, 
make  those  lines  heavy  which  represent  the  intersection  of  a 
light  and  a  dark  plane,  or  those  lines  which  cut  off  the  light — 
the  same  as  in  ordinary  mechanical  drawing. 


ENGINEERING  DRAWING 


BY 

THOMAS    E.    FRENCH 

Professor  of  Engineering  Drawing,   Ohio  State   University 


289  pages,  6x9,  over  450  illustrations,  $2.00  (8/6)  net,  postpaid 


CJ  A  general  text  on  the  language  of 
drawing,  with  distinctive  qualities  in  its 
breadth  of  scope,  thoroughness,  balance 
of  treatment,  and  logical  and  topical 
arrangement. 

€J  The  Author  has  had  an  unusual  expe- 
rience both  as  a  teacher  and  in  practice. 
He  was  assisted  by  an  especially  compe- 
tent staff  in  the  preparation  of  this  book. 

<][  It  covers  modern  practice  in  drawing 
in  every  branch  of  engineering,  empha- 
sizing the  practical  value  of  the  subject. 


MACHINE    SHOP 
DRAWINGS 


BY 

FRED  H.   COLVIN 

Managing  Editor,   "American  Machinist" 


180    pages,   4£x7,    illustrated,   $1.00    (4/6)    net,    postpaid 


CJ  A  book  intended  to  teacli  the  reading 
of  drawings  rather  than  drawing  itself. 

fl  It  explains  the  representation  of  seen 
and  unseen  portions,  the  uses  of  lines, 
and  of  different  views.  It  describes 
methods  of  laying  out  work  and  of 
simple  sketching. 

t|  The  Author  makes  use  of  a  broad 
practical  experience  in  preparing  a  splen- 
did book  for  shop  men. 

€J  It  is  a  companion  volume  to  4  c  Machine 
Shop  Mechanics"  and  uMachine  Shop 
Calculations. "  It  is  a  part  of  the  Home 
Study  Series. 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 
BERKELEY 

Return  to  desk  from  which  borrowed. 
This  book  is  DUE  on  the  last  date  stamped  below. 


DEC    3    1947 

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